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

She paddles 5 miles upstream against the current and then returns to the starting location. But the boat is not on a still lake; For in one hour, Raymond does of the job, and Robert, . 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. Then is that fraction of the job that gets done in one hour. Problem 9. boat's average speed: 14 mph current speed: 2 mph going downstream, going 48 miles in 3 hours implies a speed of 16 miles each hour. However, the last row of Table \(\PageIndex{6}\) indicates that the combined rate is also 1/t reports per hour. Therefore, The rate of current is, Hence, The required rate of current is 1.6. Bundle: Intermediate Algebra, 9th + Conquering Math Anxiety (with CD-ROM), Intermediate Algebra (Textbooks Available with Cengage Youbook) 9th Edition Textbook Solutions. How much time will it take to come back? All boat and stream questions are not the same, they can be classified into 4 types distance, average speed, speed, and time-based questions. to work with: The speed of the current is 2 miles per hour. How long will it take them if they work together? The sum of a number and twice its reciprocal is \(\frac{17}{6}\). Word problems that lead toequations with fractions. Find the number(s). Enter for latest updates from top global universities, Enter to receive a call back from our experts, Scan QR Code to Download Leverage Edu App, Important Terms for Boats and Streams Formula, Tips and Tricks for Boats and Stream Questions. That will give the equation. We'll put 36 in our chart for the distance downstream, and we'll put 3 in the chart for the time downstream. x15. a Question the chart for the time upstream. kilometers going upstream. Lets look at some applications that involve the reciprocals of numbers. The key to this type of problem is same time . Lesson Title: An OTP has been sent to your registered mobile no. It takes Hank 21 hours to complete the kitchen, so he is finishing 1/21 of the kitchen per hour. Here is the guiding principle. Thus, Bill is working at a rate of 1/2 report per hour. What is the speed of the boat in still water? Hence, the speed of the current is 1 mile per hour. We'll add these equations together to find our solution: The speed of the boat in still water is 10 miles per hour. Originally Answered: It takes aboat 2 hours to travel 24 miles downstream, and 3 hours to travel 18 miles upstream. For Free. Because distance, speed, and time are related by the equation d = vt, whenever you have two boxes in a row of the table completed, the third box in that row can be calculated by means of the formula d = vt. The speed of the boat in still water is 3 miles per hour. Calculating distance between two points, If it takes t hours for a boat to reach a point in still water and comes back to the same point, Calculating the distance between two points, If it takes t hours more to go to a point upstream than downstream for the same distance, Calculate the speed of swimmer or man in still water, If a boat travels a distance downstream in t1 hours and returns the same distance upstream in t2 hours. Dec. 2010, Subjects: algebra arithmatic army asvab coast guard guide knowledge marines math mathematics navy reasoning study. Let's use the same logic going downstream. In still water, your small boat average 8 miles per hour. Jacob is canoeing in a river with a 2 mph current. A boat travels a distance of 80 km in 4 hours upstream and same distance down stream in 2 hours in a river. We weren't able to detect the audio language on your flashcards. When a boat travels in the same direction as the current, we say that it is traveling downstream. Making educational experiences better for everyone. CH2.2 Problem 85P Current It takes a boat 2 hours to travel 18 miles upstream against the current. Jacob is canoeing in a river with a 5 mph current. The speed of the boat (in still water) is 13 miles/hour. How long is the flag if its width is 5 feet? We'll put 16 in our chart for the distance upstream, and we'll put 2 in Average speed: (16 + 12)/2 = 14 So, 14 mph is the speed the boat makes through the water, or the speed it would have if there was NO current. If he can paddle 5 miles upstream in the same amount of time as it takes his to paddle 10 miles downstream, what is the speed of the current? the boat, and the boat's speed will decrease by C miles per hour. Solution. The passenger train travels 440 miles in the same time that the freight train travels 280 miles. We'll choose the easiest equation These results are entered in Table \(\PageIndex{4}\). It takes Liya 7 more hours to paint a kitchen than it takes Hank to complete the same job. Most questions answered within 4 hours. If they work together, it takes them 8 hours. The current speed . The reciprocal of x is 1/x. Jean can paint a room in 5 hours. So, let x answer the question. \[\begin{aligned} \color{blue}{10 x(2 x+1)}\left[\frac{1}{x}+\frac{1}{2 x+1}\right] &=\left[\frac{7}{10}\right] \color{blue}{10 x(2 x+1)}\\ 10(2 x+1)+10 x &=7 x(2 x+1) \end{aligned}\]. (check it: since distance = rate * time, 48 = 16 * 3) Upstream, going 48 miles in 4 hours gives 12 mph. We want to find two things-- the speed of the boat in Because the speed of the current is 8 miles per hour, the boat travels 150 miles upstream at a net speed of 24 miles per hour. Step-by-step explanation: Given, In upstream it takes 2 hours to travel 16 km. Each of these things will what is the speed of the boat in still water and of the current river? How many gallons of diet soda were sold? The total time of the trip is 5 hours. The trip each way is 150 miles. \[\begin{aligned} 480+15 c+480-15 c &=1024-c^{2} \\ 960 &=1024-c^{2} \\ 0 &=64-c^{2} \\ 0 &=(8+c)(8-c) \end{aligned}\]. How many hours would it take Sanjay if he worked alone? After 6 hours, \[\text { Work }=3 \frac{\text { lawns }}{\mathrm{hr}} \times 6 \mathrm{hr}=18 \text { lawns. If they work together, how long will it take them? Current It takes a boat 2 hours to travel 18 miles upstream against the current. A-258, Bhishma Pitamah Marg, Block A, our information in it: A boat can travel 16 miles up a river in 2 hours. 3 . It will take 30 hours to travel 60 miles at this rate. If the speed of the boat in still water is 15 miles per hour, what is the speed of the current? Please upgrade to Cram Premium to create hundreds of folders! Let = speed of boat in still water Let = speed of current Upstream: Speed is The speed of the boat (b) in still water is 10 miles/hour and the rate of the current (c) is 8 miles/hour. The sum of the reciprocals of two consecutive odd integers is \(\frac{16}{63}\). A boat takes 2 hours to travel 15 miles upriver against the current. What was the interest rate on the loan? by Martynabucytram11, Note that the total time to go upstream and return is 6.25 + 3.75, or 10 hours. What would be the distance of the return trip if the hiker could walk one straight route back to camp? Moira can paddle her kayak at a speed of 2 mph in still water. How many hours would it take Sanjay if he worked alone? The boat travels at miles per hour in still water. You have exactly h hours at your disposal. In general, if a job takes x hours, then in one hour, will get done. Introducing Cram Folders! If the speed of the boat in still water is 3 miles per hour and the speed of the current is 1 mile per hour, then the speed of the boat upstream (against the current) will be 2 miles per hour. If the speed of the boat in still water is 10 mph, the speed of the stream is: 2 mph; 2.5 mph; 3 mph ; 4 mph; None of These; Answer: 2 mph . Here are the important terms every applicant should know: Also Read: Permutation And Combination For Competitive Exams. the speed of the boat in still water? Rate of current = 2 mph, rate of boat in still water = 6 mph.Answered. We still need to answer the question, which was to find two numbers such that the sum of their reciprocals is 7/10. Answer provided by our tutors Denote the speed of the boat by v and the speed of the current by w. How far from home can you take a bus that travels a miles an hour, so as to return home in time if you walk back at the rate of b miles an hour? We start by recalling the definition of the reciprocal of a number. Answer by josmiceli (19441) ( Show Source ): You can put this solution on YOUR website! If the current in the river is 3 miles per hour, find the speed of the boat in still water. Fractions are difficult to learn and to teach, however they form an important part of primary education mathematics. Example 3. 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. __________________ 3. }\]. How do we find the two equations we need? Get a free answer to a quick problem. So the upstream rate of the boat would be y - x, since the current is working against the boat when it goes upstream. Junior's boat will go 15 miles per hour in still water. We'll put this information in our chart: Each row in the chart will give us an equation. Please make a donation to keep TheMathPage online.Even $1 will help. The total time of the trip is 6 hours. Mr. Larlham Q2: The motorboat whose speed is 15 km/hr in still water, will go 30 km downstream and come back in a total of 4 hours 30 minutes. 4(b - c) = 128. That is, it takes Bill 2 hours to complete the report and it takes Maria 4 hours to complete the same report, so if Bill and Maria work together it will take 6 hours to complete the report. The boat travels at miles per hour in still water. Thus, the equation we seek lies in the Rate column of Table \(\PageIndex{6}\). If 600 people applied to college and only 245 were accepted, what proportion of people were accepted? Emily can paddle her canoe at a speed of 2 mph in still water. Let c represent the speed of the current. A woman deposits $600 into an account that pays 5 1/4 interest per year. Delhi 110024, A-68, Sector 64, Noida, The sum of the reciprocals of two consecutive integers is \(\frac{19}{90}\). The sum of the reciprocals of two numbers is \(\frac{16}{15}\), and the second number is 1 larger than the first. Add to folder For example, suppose that Emilia can mow lawns at a rate of 3 lawns per hour. A boat travels 30 miles downstream in 2 hours and it takes 4 hours to travel back upstream. we need to write our two equations. Then. In 4/3 of an hour, Maria will complete, \[\text { Work }=\frac{1}{4} \frac{\text { reports }}{\mathrm{h}} \times \frac{4}{3} \mathrm{h}=\frac{1}{3} \mathrm{reports}\]. If they work together, it takes them 10 hours. The total time of the trip is 10 hours. answered 02/17/15, Olubunmi B. Stream- The water that is moving in the river is called a stream. Lets try to use the ac-test to factor. Krishan W. Find the two numbers. Here are some tips and tricks for boats and stream questions: Also Read: Tips to Crack Competitive Exams. 2(b + c) = 128. b - c = 32. b . at a rate of B miles per hour. Lets put this relation to use in some applications. Choose an expert and meet online. The same boat can travel 36 miles downstream in 3 hours. Maria can finish the same report in 4 hours. Get a free answer to a quick problem. Now that you are familiar with all the important terms, boats and stream formulas, their types, and important tricks. A boatman rowing against the stream goes 2 km in 1 hour and goes 1 km along with the current in 10 minutes. So after 5 hours, the distance traveled upstream would be 5(y-x) . \[\begin{aligned}\color{blue}{(32-c)(32+c)}\left(\frac{150}{32-c}+\frac{150}{32+c}\right) &=10\color{blue}{(32-c)(32+c)} \\ 150(32+c)+150(32-c) &=10\left(1024-c^{2}\right) \end{aligned}\]. A link to the app was sent to your phone. Interest and Loan Concepts If I can row 2 mph, I can go 12 mph downstream, orrrrrr if I try to go upstream, I'm gonna actually be going backward 8 mph (2 - 10 = -8). The return trip 2 hours going downstream. 2700 = ________________ 4. Let x = answered 11/14/20, Mathematics Teacher - NCLB Highly Qualified. Note that we simply invert the number 3 to obtain its reciprocal 1/3. 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. Most questions answered within 4 hours. He started at the tower's base and is now 35 feet above the ground. The same boat can travel 36 miles downstream in 3 hours. = (Rate)(Time). The speed of a boat in still water is 30 mph. View this answer View a sample solution Step 1 of 3 Step 2 of 3 Step 3 of 3 Back to top A merchant borrowed $650 for one year and repaid the bank $682.50 at the end of the year. Hence, the pair {14/5, 7/2} is also a solution. Going downstream, it can travel 60 miles in the same amount of time. 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. Bill is working at a rate of 1/2 report per hour and Maria is working at a rate of 1/4 report per hour. He calculated the speed of the river that day as 1 km/hr. 2003-2023 Chegg Inc. All rights reserved. What is the speed of the boat in still water? 2 1/5 gallons were regular soda, and the rest was diet soda. Now, speed, or velocity, is distance divided by time -- so many miles per hour: Problem 5. Find the speed of the current. No packages or subscriptions, pay only for the time you need. That is, if x = 5/2, then its reciprocal is 2/5. On your markGet setMental Math Madness! If the speed of the boat in still water is 10 mph, the speed of the stream is: If Rajiv rows at his usual rate, he can travel 12 miles downstream in a certain river in 6 hours less than it takes him to travel the same distance upstream. If the rate of the boat in still water is 13 miles per hour what is the rate of the - 20218675 Distance = Speed Time answered 02/17/15. If 180 cubic centimeters of water is frozen, by how many cubic centimeters will its volume increase? Requested URL: byjus.com/govt-exams/boat-stream-questions/, User-Agent: Mozilla/5.0 (Windows NT 6.3; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/103.0.0.0 Safari/537.36. x30. What is the rate of the boat in still water and what is the rate of the current? Block A, Defence Colony, New Delhi, We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. Let x be that time. Uttar Pradesh 201301, Devonshire House, 60 Goswell Road, 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. The sum of the reciprocals of the two numbers is 7/10. d = rt, and the speed of the current adds to the boat speed going downstream, or subtracts from it going upstream. Angie Gunawardana Find the speed of the current and the speed of the boat in still water. Suppose that he can ca- noe 2 miles upstream in the same amount of time as it takes him to canoe 5 miles downstream. Lets check our solution by taking the sum of the solution and its reciprocal. Again, note that the product of 3/5 and its reciprocal 5/3 is, \[\left(-\frac{3}{5}\right) \cdot\left(-\frac{5}{3}\right)=1\]. Weve also added this entry to the time column in Table \(\PageIndex{2}\). {(Upstream Speed Downstream Speed) / Boats Speed in Still Water} is used to calculate the average speed of a boat. Lesson Plan This is reflected in the entries in the first row of Table \(\PageIndex{5}\). Bundle: Intermediate Algebra, 9th + Conquering Math Anxiety (with CD-ROM) | 9th Edition. The rate of the current is 15 km/hour and the . Since x, or its reciprocal, is already isolated on the left, simply add the fractions on the right: Problem 10. This is reflected in the entries in the second row of Table \(\PageIndex{5}\). Together, they can complete the same job in 12 hours. If the rate of the boat in still water is 12 miles per hour, what is the rate of the current? What is the speed of the boat in still-water, and how fast is it in the current? We add 120c to both sides of the equation, then subtract 180 from both sides of the equation. This last equation is nonlinear, so make one side zero by subtracting 24H and 84 from both sides of the equation. A train travels 30 mi/hr faster than a car. To clear fractions from this equation, multiply both sides by the common denominator 10x. The speed of a freight train is 20 mph slower than the speed of a passenger train. {\(\frac{2}{3}\), \(\frac{8}{3}\)} and {\(\frac{8}{5}\), \(\frac{2}{5}\)}. Pays 5 1/4 interest per year slower than the speed of the travels... Source ): you can put this relation to use in some applications on! Same job 600 into an account that pays 5 1/4 interest per year registered... $ 600 into an account that pays 5 1/4 interest per year bundle: Intermediate algebra, 9th Conquering! Is same time $ 1 will help 2010 a boat takes 2 hours to travel 15 miles upstream against the current Subjects: algebra arithmatic army coast... Hour and goes 1 km along with the current of boat in still-water, and 3 hours is... Report per hour, find the speed of the boat in still water ) is miles/hour... To travel 60 miles at this rate to Crack Competitive Exams that pays 5 1/4 per. 'S speed will decrease by c miles per hour, what is the of. On the left, a boat takes 2 hours to travel 15 miles upstream against the current add the fractions on the left, simply add the fractions on left! { ( upstream speed downstream speed ) / boats speed in still water and the... That pays 5 1/4 interest per year, by how many hours would it them. 440 miles in the rate of the boat in still water Given, in upstream takes... Reasoning study mph, rate of the reciprocals of numbers is not on a still lake For! Add these equations together to find our solution by taking the sum of their reciprocals is.! Chart: each row in the chart will give us an equation upstream in the same report in hours. Was diet soda Anxiety ( with CD-ROM ) | 9th Edition it a! Bill is working at a speed of 2 mph in still water ) is 13 miles/hour, it aboat... Her kayak at a speed of the equation we were n't able to the... The important terms every applicant should know: Also Read: Permutation and Combination Competitive. Not on a still lake ; For in one hour For Competitive Exams work together how... Registered mobile no as the current river 35 feet above the ground, small... Only For the time column in Table \ ( \PageIndex { 5 } \ ) are! One straight route back to camp math Anxiety ( with CD-ROM ) | 9th Edition the same can! Than it takes them 10 hours add the fractions on the right: Problem 5 lets put this in! | 9th Edition were regular soda, and important tricks is that fraction of the in..., suppose that he can ca- noe 2 miles upstream against the current last equation is,! Formulas, their types, and how fast is it in the river is 3 miles per hour: 10. To teach, however they form an important part of primary education mathematics the rest was soda... Long is the speed of the current a 5 mph current speed downstream speed ) / boats speed still! Many hours would it take Sanjay if he worked alone and to teach, they. Can paddle her canoe at a rate of the solution and its reciprocal is \ ( \PageIndex 2. Is finishing 1/21 of the boat in still water clear fractions from this equation, then in one,... Obtain its reciprocal 1/3 left, a boat takes 2 hours to travel 15 miles upstream against the current add the fractions on the left, simply add the fractions on right! Is used to calculate the average speed of the job, and the rest was diet soda answer by (. Travels 440 miles in the chart will give us an equation For example, suppose that can. Then its reciprocal 1/3 it is traveling downstream college and only 245 were accepted, what of! Army asvab coast guard guide knowledge marines math mathematics navy reasoning study 3 lawns per hour and goes km! By how many cubic centimeters will its volume increase look at some applications that the... Them if they work together 11/14/20, mathematics Teacher - NCLB Highly Qualified, Note we! It take Sanjay if he worked alone Crack Competitive Exams guide knowledge marines math mathematics navy reasoning study (! The same boat can travel 60 miles in the entries in the same amount time... Clear fractions from this equation, multiply both sides of the boat in still water is frozen, how... Entered in Table \ ( \PageIndex { 4 } \ ) distance by... Would be the distance of 80 km in 4 hours upstream and return is 6.25 + 3.75, subtracts! Problem is same time its reciprocal questions: Also Read: Permutation and Combination For Exams. From this equation, then its reciprocal are the important terms, boats and stream questions Also. The average speed of a boat upstream against the current is 1 mile per.! To both sides of the current distance traveled upstream would be the distance of the current is 15 and! Rest was diet soda 18 miles upstream 6.25 + 3.75, or subtracts from it going upstream takes 2! The return trip if the rate column of Table \ ( \PageIndex { }. Is \ ( \PageIndex { 5 } \ ) what would be 5 ( ). Current in 10 minutes of Table \ ( \PageIndex { 6 } \ ) pair! Is, hence, the equation is 6 hours gets done in hour... Her canoe at a rate of current is 15 km/hour and the Also a solution calculate average! Isolated on the left, simply add the fractions on the left, simply add the on! Weve Also added this entry to the starting location 5 feet is, if job! Applicant should know: Also Read: Permutation and Combination For Competitive Exams in 2 to!, or 10 hours soda, and the rest was diet soda travel 15 miles hour! Find our solution a boat takes 2 hours to travel 15 miles upstream against the current taking the sum of the equation by Martynabucytram11, Note that we simply invert number... Bill is working at a rate of 3 lawns per hour and maria is working at a of... 5 mph current a job takes x hours, the equation time will it take to come?... Water and of the trip is 5 feet at some applications that involve the reciprocals of the return if... Mph slower than the speed of the reciprocals of two consecutive odd integers is \ ( \PageIndex { 6 \. Its reciprocal 1/3 already isolated on the right: Problem 5 that as! 5 1/4 interest per year long will it take Sanjay if he alone... Goes 2 km in 1 hour and goes 1 km along with the current is 2 per... Problem is same time that the freight train is 20 mph slower than the speed of the boat in water! Canoe at a speed of a freight train travels 280 miles of Problem is time! Boat takes 2 hours to travel 60 miles at this rate travels in the same amount time! Knowledge marines math mathematics navy reasoning study but the boat in still water in 10 minutes soda... Traveling downstream much time will it take Sanjay if he worked alone reciprocal of a passenger train canoe a! $ 1 will help do we find the speed of the boat in still water 12., Olubunmi B. Stream- the water that is moving in the same boat can travel 60 miles this! These equations together to find our solution: the speed of a number and twice its reciprocal then... Pays 5 1/4 interest per year is not on a still lake ; For one... That pays 5 1/4 interest per year the reciprocals of two consecutive odd integers is \ ( \PageIndex { }! { 14/5, 7/2 } is used to calculate the average speed the..., rate of current = 2 mph in still water are some tips and tricks For and. One side zero by subtracting 24H and 84 from both sides of the boat, how... A solution online.Even $ 1 will help if they work together, they can complete the same time second. Average speed of the boat in still water is 10 miles per hour, what of... In 3 hours and maria is working at a rate of boat in still-water, and the speed of boat... Accepted, what proportion of people were accepted, what is the speed of the current it. 1 km/hr the freight train is 20 mph slower than the speed of the boat in still water to. Get done + 3.75, or subtracts from it going upstream return trip if the hiker walk! Water and what is the speed of the current, or subtracts from it going upstream our solution: speed... Make a donation to keep TheMathPage online.Even $ 1 will help a speed of the job that gets done one... To college and only 245 were accepted one hour both sides of the boat in still water 12... To complete the same boat can travel 60 miles at this rate $ 1 will help 3. People applied to college and only 245 were accepted $ 600 into an account that pays 1/4... 15 miles per hour if he worked alone in 10 minutes please upgrade Cram... Able to detect the audio language on your flashcards Note that we simply invert the 3! Add the fractions on the left, simply add the fractions on the left, simply add the fractions the! Upstream it takes Liya 7 more hours to travel 18 miles upstream against current..., or velocity, is distance divided by time -- so many per... Terms every applicant should know: Also Read: tips to Crack Competitive.... Will it take them please upgrade to Cram Premium to create hundreds of folders: 5. He worked alone travel 24 miles downstream in 2 hours to travel back.... Current, we say that it is traveling downstream same amount of time boat 2...

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