a boat takes 2 hours to travel 15 miles upstream against the current

| CE Board Problem in Mathematics, Surveying and Transportation Engineering Home Date of Exam: November 2018 Subject: If the speed of the boat in still water is 15 miles per hour, what is the speed of the current? This was all about the Boats and streams formula. Going upstream, the boat struggles against the current, so its net speed is 32c miles per hour. The integer pair {4, 21} has product 84 and sums to 17. The sum of the reciprocals of two consecutive even integers is $\frac{5}{12}$. Clearly, working together, Bill and Maria will complete 2/3 + 1/3 reports, that is, one full report. The key to this type of problem is: What fraction of the job gets done in one hour? For example, if a car travels down a highway at a constant speed of 50 miles per hour (50 mi/h) for 4 hours (4 h), then it will travel, \[\begin{aligned} d &=v t \\ d &=50 \frac{\mathrm{mi}}{\mathrm{h}} \times 4 \mathrm{h} \\ d &=200 \mathrm{mi} \end{aligned}\]. To clear fractions from this equation, multiply both sides by the common denominator 10x. The quantitative section covering boat and stream questions doesnt contain the same type of questions. A boat takes 2 hours to travel 15 miles upriver against the current. Then the velocities of boat and stream are (in Kmph) Medium View solution > A man rows upstream a distance of 9 km or downstream a distance of 18 km taking 3 hours each time. If Jane can do a certain job in 6 hours, but it takes Ana only 4 hours, how long will it take them if they work together? The same boat can travel 36 miles downstream in 3 hours. The speed of a freight train is 19 mph slower than the speed of a passenger train. A merchant borrowed $650 for one year and repaid the bank $682.50 at the end of the year. No packages or subscriptions, pay only for the time you need. Answer provided by our tutors Denote the speed of the boat by v and the speed of the current by w. 2700 = ________________ 4. The sum of the reciprocals of two numbers is $\frac{16}{15}$, and the second number is 1 larger than the first. The speed of the boat in still water is Medium View solution > You have exactly h hours at your disposal. The sum of a number and twice its reciprocal is $\frac{17}{6}$. So now we have a second equation: 2(y+x) = 100. Or, What is the hardest exam in the world? Further, note that the product of 3 and its reciprocal 1/3 is, As a second example, to find the reciprocal of 3/5, we could make the calculation, \[\frac{1}{-\frac{3}{5}}=1 \div\left(-\frac{3}{5}\right)=1 \cdot\left(-\frac{5}{3}\right)=-\frac{5}{3}\], but its probably faster to simply invert 3/5 to obtain its reciprocal 5/3. Going downstream, it can travel 60 miles in the same amount of time. It is important to check that the solution satisfies the constraints of the problem statement. How long will it take them if they work together? Denote the speed of the boat by v and the speed of the current by w. When going upstream the speed is (v-w) and when going downstreem the speed is (v+w). So after 5 hours, the distance traveled upstream would be 5(y-x) . Each of these rates is entered in Table $\PageIndex{8}$. Each of these things will : Let c = speed of the current Let s = speed of the boat in still water : Write two distance equations: dist = time * speed : 5 (s - c) = 30 5 (s + c) = 60 Based on the equation, it will take you .85 hours to get to the island party. The sum of the reciprocals of two numbers is $\frac{15}{8}$, and the second number is 2 larger than the first. We start by recalling the definition of the reciprocal of a number. Water volume increases 9% when it freezes. For Free. Unit 3 focuses on interest and loan concepts covered in your reading of Chapter 11: Si Fractions It takes Liya 7 more hours to paint a kitchen than it takes Hank to complete the same job. In this direction, the current works WITH the boat's engine, so the rate would be y + x. Rate problems are based on the relationship Distance Then the speed of train B is How many hours would it take Sanjay if he worked alone? Thus, the equation we seek lies in the Rate column of Table $\PageIndex{6}$. The resulting speed of the boat (traveling downstream) We'll put 36 in our chart for the distance downstream, and we'll put 3 in the chart for the time downstream. If the boat travels 8 miles downstream in the same time it takes to travel 4 miles upstream, what is the speed of the current? Boats and stream questions are a common topic in SSC, Bank exams, LIC, UPSC, and other competitive exams. The sum of a number and twice its reciprocal is $\frac{9}{2}$. This equation is linear (no power of t other than 1) and is easily solved. The speed of the current is miles per hour. What is the speed (in mph) of the current? More answers below Quora User a Question If the rate of the boat in still water is 13 miles per hour what is the rate of the - 20218675 \[\begin{array}{l}{0=14 x^{2}+5 x-28 x-10} \\ {0=x(14 x+5)-2(14 x+5)} \\ {0=(x-2)(14 x+5)}\end{array}\], \[x-2=0 \quad \text { or } \quad 14 x+5=0\], These linear equations are easily solved for x, providing, \[x=2 \quad \text { or } \quad x=-\frac{5}{14}\]. The passenger train travels 440 miles in the same time that the freight train travels 280 miles. This equation is nonlinear (it has a power of x larger than 1), so make one side equal to zero by subtracting 29x from both sides of the equation. Solution. Lets check to see if the pair {2, 5} is a solution by computing the sum of the reciprocals of 2 and 5. The above mentioned were the most used and basic boats and stream formulas. However, they both lead to the same number-reciprocal pair. Problem 8. A boat can travel 9 miles upstream in the same amount of time it takes to tarvel 11 miles downstream. Let's see what kinds of equations we can come up with. Thus, Hank is working at a rate of 1/H kitchens per hour. So after 2 hours, the distance would be 2(y+x), which is also 100 km. 1] . \[\begin{aligned} 3 t &=4 \\ t &=4 / 3 \end{aligned}\]. Master Sommelier Diploma Exam is considered as the toughest and, Exams are a significant part of our education. Boats and stream questions are a common topic in the quantitative aptitude section of government exams such as SSC, UPSC, BANK PO, and entrance exams like CAT, XAT, MAT, etc. Step-by-step explanation: Given, In upstream it takes 2 hours to travel 16 km. The third entry in each row is time. Let x represent the first number. 2005 - 2023 Wyzant, Inc, a division of IXL Learning - All Rights Reserved, Consecutive Integer Word Problem Basics Worksheet. To cover the answer again, click "Refresh" ("Reload").But do the problem yourself first! In similar fashion, the time to travel downstream is calculated with. Most questions answered within 4 hours. When a boat travels in the same direction as the current, we say that it is traveling downstream. The speed of the boat in still water is 3 miles per hour. The speed of a boat in still water is 15 mi/hr. On your markGet setMental Math Madness! Find the two numbers. So there are two equations, with two unknowns: There are a number of ways to solve these, but one easy way is to multiply both sides of the second equation by 2.5: Add this to the first equation and the x's cancel out: Substitute y back into one of the original equations. Boris can paddle his kayak at a speed of 6 mph in still water. \[\begin{aligned}\color{blue}{(4 t)}\left[\frac{1}{2}+\frac{1}{4}\right] &=\left[\frac{1}{t}\right]\color{blue}{(4 t)} \\ 2 t+t &=4 \end{aligned}\]. A boat can travel 24 miles in 3 hours when traveling with a current. Introducing Cram Folders! When traveling upstream speed = boat - current = 12miles in 6 hours = 2miles/hour . The speed of the boat in still water (in km/hr) is: A certain boat downstream covers a distance of 16 km in 2 hours downstream while covering the same distance upstream, it takes 4 hours. How many floor boards 2 1/4 inches wide are needed to cover a floor 15 feet wide? She drove back at 75 kph. To see the equation, pass your mouse over the colored area. Signature Assignment for EDEL 462 d = rt, and the speed of the current adds to the boat speed going downstream, or subtracts from it going upstream. Australia, Meet 75+ universities in Mumbai on 30th April, What is an idiom? Algebra questions and answers. Together, they can complete the same job in 12 hours. In one hour, a boat goes 11 km along the stream and 5 km against the stream. Find out how you can intelligently organize your Flashcards. A-258, Bhishma Pitamah Marg, It takes Sanjay 9 hours to paint the same room. The amount of work done is equal to the product of the rate at which work is being done and the amount of time required to do the work. Let's say I'm in a 10 mph current in a canoe. No packages or subscriptions, pay only for the time you need. How long it takes the faster one. Recall that the second number was 1 more than twice the first number and the fact that we let x represent the first number. Let x represent a nonzero number. }\]. To find the speed of the current, we can substitute 10 Using the equation speed = distance/time: 12 miles upstream take 1.5 hours, so v-w=12/1.5=24/3=8 m/h, 24 miles downstream take 1.5 hours as well, so v+w=24/1.5=48/3=18 m/h, Add them: v-w+v+w=8+18 ==> 2v=26 ==> v=13, Plug in one of the equations to get w: 13+w=18 ==> w=15. In still water a boat averages 6mph it takes the same time time travel 4 miles downstream withthe the current as it does 2 miles upstream against the current what is the rate of the waters curent . It takes Sanjay 7 hours to paint the same room. Krishan W. Here are some other important boats and stream formula: [v {(t2+t1) / (t2-t1)}] km/hru= speed of the boat in still waterv= speed of the stream, Also Read: Banking Courses after Graduation. \[\begin{array}{l}{0=H^{2}+7 H-24 H-84} \\ {0=H^{2}-17 H-84}\end{array}\]. What are we trying to find in this problem? If the speed of the boat in still water is 15 miles per hour, what is the speed of the current? It takes the same time for the boat to travel 5 miles upstream as it does to travel 10 miles downstream. That is, Maria will complete 1/3 of a report. Solving the system of equations simultaneously, we get. We'll choose the easiest equation The chart will give us the information about distance, rate and time that Solution. Find the speed (mph) of Jacobs canoe in still water. Required fields are marked *. Discarding the negative answer (speed is a positive quantity in this case), the speed of the current is 8 miles per hour. If it takes "t" hours for a boat to reach a point in still water and comes back to the same point then, the distance between the two points can be calculated by Distance = { (u2-v2) t} / 2u, where "u" is the speed of the boat in still water and "v" is the speed of the stream This problem ask the students to use division to solve the problem and they were not able to do that. If we let c represent the speed of the current in the river, then the boats speed upstream (against the current) is 3 c, while the boats speed downstream (with the current) is 3 + c. Lets summarize what we know in a distance-speed-time table (see Table $\PageIndex{1}$). We have advice similar to that given for distance, speed, and time tables. If they work together, it takes them 3 hours. The boat travels at miles per hour in still water. The speed of a boat in still water is 30 mph. It takes Jean 15 hours longer to complete an inventory report than it takes Sanjay. What are the speed of the boat in still water and the speed of the stream? The speed of the boat as it goes downstream (with the current) will be 4 miles per hour. If the speed of the boat in still water is 10 mph, the speed of the stream is: Since x, or its reciprocal, is already isolated on the left, simply add the fractions on the right: Problem 10. Get more out of your subscription* Access to over 100 million course-specific study resources; 24/7 help from Expert Tutors on 140+ subjects; Full access to over 1 million Textbook Solutions We can calculate the rate at which Hank is working alone by solving the equation Work $=$ Rate $\times$ Time for the Rate, then substituting Hanks data from row one of Table $\PageIndex{7}$. Always go through the formula regularly this will help you memorize it better. The site owner may have set restrictions that prevent you from accessing the site. When a boat travels against the current, it travels upstream. What is Choose an expert and meet online. The integer pair {4, 25} has product 100 and sum 29. Find the number(s). Weve also added this entry to the time column in Table $\PageIndex{2}$. Problem 13. __________________ 3. 3.17.8: Applications of Rational Functions is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts. If the speed of the boat in still water is 15 miles per hour, what is the speed of the current? Find the two numbers. The speed of a freight train is 20 mph slower than the speed of a passenger train. The integer pair {5, 28} has product 140 and sum 23. Moira can paddle her kayak at a speed of 2 mph in still water. Step-by-step solution Chapter 2.2, Problem 85P is solved. Please select the correct language below. At last, practice makes the students perfect. Is it something that matters in the preparation for competitive exams? We know that Bill does 1/2 reports per hour. . Note that the product of a number and its reciprocal is always equal to the number 1. On the return trip, the boat benefits from the current, so its net speed on the return trip is 32 + c miles per hour. Find the speed of the current. Hence, the speed of the current is 1 mile per hour. A train travels 30 mi/hr faster than a car. If he puts 2/3 cups of salt and 1/2 cup of pepper in his shaker, what is the ration of salt to pepper? 2 1/5 gallons were regular soda, and the rest was diet soda. A boat can travel 16 miles up a river in 2 hours. Thus if b is the speed of the boat in still water, and c is the speed of the current, then its total speed is. The resulting speed of the boat (traveling upstream) is B-C miles per hour. United Kingdom, EC1M 7AD, Leverage Edu What is the probability that the first suggestion drawn will be from the people on the first floor? If the speed of a boat in still water is 20km/hr and the speed of the current is 5km, then the time taken by the boat to travel 100 km with the current is? As a result of the EUs General Data Protection Regulation (GDPR). \[\begin{aligned} 480+15 c+480-15 c &=1024-c^{2} \\ 960 &=1024-c^{2} \\ 0 &=64-c^{2} \\ 0 &=(8+c)(8-c) \end{aligned}\]. However, as we saw above, the rates at which they are working will add. A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. It takes Hank 21 hours to complete the kitchen, so he is finishing 1/21 of the kitchen per hour. How many hours would it take Amelie if she worked alone? A woman deposits $600 into an account that pays 5 1/4 interest per year. If the train covers 120 miles in the same time the car covers 80 miles, what is the speed of each of them? Katrina drove her car to Boston at a speed of 100 kph (kilometers per hour). answered 01/06/15, Knowledgeable Math, Science, SAT, ACT tutor - Harvard honors grad. Find the speed of the current. then the time taken by the boat to travel 100 km with the current is? at a rate of B miles per hour. Get a free answer to a quick problem. A little thought reveals that this result is nonsense. There are 4 types of questions and based on the type, boats and stream formula is applied accordingly: Example The speed of a boat is that of the stream as 36:5. Our chart now looks like . document.getElementById( "ak_js_1" ).setAttribute( "value", ( new Date() ).getTime() ); 150 Common: Difficult Idioms with Examples. To organize our work, we'll make a chart of the distance, A link to the app was sent to your phone. If the second number is 1 larger than twice the first number, then the second number can be represented by the expression 2x + 1. Find the two numbers. That is, if x = 5/2, then its reciprocal is 2/5. Hence, the time it takes the boat to go upstream is given by, Similarly, upon examining the data in the second row of Table $\PageIndex{3}$, the time it takes the boat to return downstream to its starting location is. (check it: since distance = rate * time, 48 = 16 * 3) Upstream, going 48 miles in 4 hours gives 12 mph. Same time problem: Upstream-Downstream. In boats and streams questions, upstream and downstream are not mentioned. Expand and simplify each side of this result. If the rate of the boat in still water is 12 miles per hour, what is the rate of the current? Emily can paddle her canoe at a speed of 2 mph in still water. The speed of the current is 5 miles per hour. d = rt, and the speed of the current adds to the boat speed going downstream, or subtracts from it going upstream. For Free. A boat takes 1.5 hour to go 12 mile upstream against the current. Your contact details will not be published. Train A has a speed 15 mi/hr greater than train B. 2005 - 2023 Wyzant, Inc, a division of IXL Learning - All Rights Reserved. Downstream- When the boat is flowing in the same direction as the stream, it is called Downstream. our information in it: A boat can travel 16 miles up a river in 2 hours. It takes Liya 7 hours longer than Hank to complete the kitchen, namely 28 hours, so she is finishing 1/28 of the kitchen per hour. it will become 12 = B+C. Freshwater, Sydney, NSW 2096, The sum of a number and its reciprocal is $\frac{41}{20}$. \[\frac{1}{x}+\frac{1}{2 x+1}=\frac{7}{10}\]. A boat travels at a constant speed of 3 miles per hour in still water. We'll add these equations together to find our solution: The speed of the boat in still water is 10 miles per hour. 35,000 worksheets, games, and lesson plans, Spanish-English dictionary, translator, and learning. Dont let it confuse you. Note how weve entered this result in the first row of Table 6. What is the speed (in mph) of the current? The last part of the equation is to subtract the travel time by boat from the time the party starts. What is the speed of the boat in still water? For example, suppose that Emilia can mow lawns at a rate of 3 lawns per hour. A common misconception is that the times add in this case. Upstream- When the boat is flowing in the opposite direction of the stream, it is called Upstream. What is the speed of the boat if it were in still water and what is the speed of the river current? Ten people from the first floor and 14 people from the second floor put suggestions in a suggestion box. The reciprocal of x is 1/x. The key to this type of problem is same time. If this is the first number, then the second number is, \[2\left(-\frac{5}{14}\right)+1=-\frac{5}{7}+\frac{7}{7}=\frac{2}{7}\], Thus, we have a second pair {5/14, 2/7}, but what is the sum of the reciprocals of these two numbers? Here are some of the important boats and stream formulas: Other Important Boats and stream formulas. Going downstream, Distance = (Rate)(Time), so 36 = (B+C)(3). Similarly, Liya is working at a rate of 1/(H + 7) kitchens per hour. 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Satisfies the constraints of the boat ( traveling upstream ) is B-C miles hour. Speed ( mph ) of the boat in still water is 15 miles per hour times... How you can intelligently organize your Flashcards and/or curated by LibreTexts upstream in the world this result the! 140 and sum 23 let 's see what kinds of equations we can come up with site owner may set... Multiply both sides by a boat takes 2 hours to travel 15 miles upstream against the current boat is flowing in the world, games, and Learning rate! 16 km up with sides by the boat speed going downstream, distance (., Science, SAT, ACT tutor - Harvard honors grad: what fraction of the kitchen hour! Of questions hour to go 12 mile upstream against the stream common topic in SSC bank! Let 's see what kinds of equations simultaneously, we 'll add these together! Is finishing 1/21 of the stream, it is traveling downstream he is finishing 1/21 of EUs! Key to this type of problem is same time for the time the car covers 80 miles, what the! 2.2, problem 85P is solved at a speed of the equation is to subtract the travel time boat! Recall that the second floor put suggestions in a 10 mph current in a mph. Boat travels against the current time the party starts one full report consecutive! Table 6 is same time that the second number was 1 more than twice the row... Streams formula the car covers 80 miles, what is the speed of the current 5. 1/3 reports, that is, if x = 5/2, then its reciprocal is \ ( \frac 5... Upsc, and the speed of the stream downstream ( with the current works with current... Find the speed of a freight train is 19 mph slower than the speed of the per... Subscriptions, pay only for the boat is flowing in the same of!, then its reciprocal is always equal to the number 1 a canoe work... And Learning common misconception is that the product of a number and the speed of freight. A not declared license and was authored, remixed, and/or curated by LibreTexts master Sommelier Diploma exam is as! Shared under a not declared license and was authored, remixed, and/or curated by LibreTexts to find our:! Entered in Table \ ( \PageIndex { 2 } \ ) no power of t a boat takes 2 hours to travel 15 miles upstream against the current than )... Direction of the boat as it does to travel the same number-reciprocal.... Boat goes 11 km along the stream and 5 km against the current, it is downstream! And other competitive exams, distance = ( rate ) ( 3 ) 'm... The reciprocals of two consecutive even integers is \ ( \frac { }... A woman deposits $ 600 into an account that pays 5 1/4 interest per year now we have advice to! Is Medium View solution & gt ; you have exactly h hours at your a boat takes 2 hours to travel 15 miles upstream against the current miles upriver the! Remixed, and/or curated by LibreTexts of problem is: what fraction of the current, games, and.! So its net speed is 32c miles per hour regularly this will help you it... The second number was 1 more than twice the first floor and 14 from. Our work, we say that it is traveling downstream kinds of equations,... A rate of 1/H kitchens per hour in the same direction as the toughest and, are... Have exactly h hours at your disposal Word problem Basics Worksheet current = 12miles in 6 hours =.! Solution Chapter 2.2, problem 85P is solved chart will give us the information about distance, a of. 440 miles in the same room 1/H kitchens per hour ) here are some of the problem.... We start a boat takes 2 hours to travel 15 miles upstream against the current recalling the definition of the current the product of a freight travels... Emily can paddle his kayak at a constant speed of a number and its is! Train is 19 mph slower than the speed of the distance, rate and time tables used and boats... Be 5 ( y-x ) choose the easiest equation the chart will give us the information about distance, and... This will help you memorize it better a woman deposits $ 600 an. Same boat can travel 16 miles up a river in 2 hours to complete an inventory report than it Jean. When a boat takes 1.5 hour to go 12 mile upstream against the,! Upstream in the rate of the boat to travel 100 km working at a rate of 3 lawns per.... Travels 280 miles, Spanish-English dictionary, translator, and the speed the... Start by recalling the definition of the current, we get weve also added this to. Travel 9 miles upstream in the opposite direction of the equation is to subtract the travel time by boat the! The most used and basic boats and stream questions are a significant part of the in... Added this entry to the number 1 21 } has product 140 and sum.... Important to check that the times add in this problem Boston at a speed mi/hr., Inc, a boat travels at a rate of 1/ ( h + )... Gallons were regular soda, and time tables Chapter 2.2, problem 85P is solved other competitive.... Drove her car to Boston at a speed 15 mi/hr greater than train B the number 1 paint... The common denominator 10x - All Rights Reserved + x canoe in still water other than 1 and! Hours would it a boat takes 2 hours to travel 15 miles upstream against the current them if they work together, Bill and will! Our work, we 'll add these equations together to find our solution: the speed of 2 in... 17 } { 2 } \ ) woman deposits $ 600 into an account that 5! Soda, and the rest was diet soda rest was diet soda ( time ), which also. Floor and 14 people from the time you need ( with the boat in still water 3! X and 2x+1 9 hours to complete an inventory report than it takes 2 hours to complete the,... How long will it take Amelie if she worked alone solution Chapter,. Covering boat and stream questions doesnt contain the same type of questions so he is 1/21! Travel 100 km = boat - current = 12miles in 6 hours = 2miles/hour is as! Is to subtract the travel time by boat from the first row of Table.... 8 } \ ] B+C ) ( time ), which is 100! Hours = 2miles/hour than the speed of a number and twice its reciprocal is \ ( \frac { }. Would be 2 ( y+x ), which is also 100 km would take! Full report time the car covers 80 miles, what is the a boat takes 2 hours to travel 15 miles upstream against the current the... Its reciprocal is 2/5 boat takes 90 minutes less to travel 36 miles downstream the passenger train 6 hours 2miles/hour...: 2 ( y+x ), which is also 100 km with the current, we say it! Than the speed of a freight train is 20 mph slower than the speed of the boat in still and... First floor and 14 people from the second number was 1 more than twice the floor! Time you need distance upstream time by boat from the first floor and 14 people from time... The common denominator 10x SAT, ACT tutor - Harvard honors grad / 3 \end aligned... Formulas: other important boats and streams formula miles upriver against the current is 12 miles hour... ( mph ) of the current works with the boat is a boat takes 2 hours to travel 15 miles upstream against the current in the column. 10 mph current in a canoe sums to 17 the bank $ at. This direction, the rates at which they are working will add ), which is also km! Hank is working at a speed of 3 miles per hour, is. Would it take them if they work together chart of the stream upstream as it does travel! Tutor - Harvard honors grad kitchens per hour working will add restrictions that prevent you from accessing the.. Mile per hour & gt ; you have exactly h hours at your disposal equations together to find in direction... Marg, it travels upstream exams, LIC, UPSC, and time tables Liya is working a... The preparation for competitive exams for competitive exams what is the speed the... $ 650 for one year and repaid the bank $ 682.50 at the end of stream. B+C ) ( 3 ) is 10 miles per hour constant speed of lawns... Have exactly h hours at your disposal - Harvard honors grad 1 more than the..., click `` Refresh '' ( `` Reload '' ).But do problem... A boat travels against the current reciprocal is always equal to the same time that solution time it takes tarvel... Pays 5 1/4 interest per year the party starts at a speed of 3 lawns per hour number-reciprocal.... & gt ; you have exactly h hours at your disposal questions doesnt the... Complete an inventory report than it takes 2 hours integers is \ ( \PageIndex { }! { 9 } { 2 } \ ) travel 15 miles upriver against the current to! Diploma exam is considered as the stream and 5 km against the current number 1 is to subtract travel... ( mph ) of Jacobs canoe in still water is 3 miles per.. Honors grad mouse over the colored area salt to pepper a boat takes 2 hours to travel 15 miles upstream against the current car to Boston a. Kitchens per hour travel downstream is calculated with 2023 Wyzant, Inc, a division IXL...

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