For example, suppose that Emilia can mow lawns at a rate of 3 lawns per hour. Problem 12. \[Rate \(=\frac{\text { Work }}{\text { Time }}=\frac{1 \text { report }}{t \mathrm{h}}\)\]. On the other hand, if x = 2/5, then its reciprocal is 5/2. 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. Consequently, if the first number is x = 2, then the second number is 2x + 1, or 2(2) + 1. Thus, Hank is working at a rate of 1/H kitchens per hour. Making educational experiences better for everyone. His speed of the boat in still water is 3 km/hr. Choose an expert and meet online. Jon P. Lesson Plan Let c represent the speed of the current. Find the rate of the current and the rate of the boat in still water. There are two numbers. The total time of the trip is 10 hours. Legal. It will take 15 hours to travel 60 miles at this rate. The sum of the reciprocals of two consecutive integers is \(\frac{19}{90}\). The integer pair {4, 21} has product 84 and sums to 17. The trip each way is 150 miles. We can make the numbers a bit smaller by noting that both sides of the last equation are divisible by 10. 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. How long does it take him to go 5 km in stationary water? Break up the middle term of the quadratic trinomial using this pair, then factor by grouping. it's moving upstream and downstream on a river. Note that the product of a number and its reciprocal is always equal to the number 1. Since we are told that in still water (no current), the boat would be making 12 mph, it follows therefore that the current's speed must be the difference of 12 - 7.5, or 4.5 mph. 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? Example A boat, while going downstream in a river covered a distance of 50 miles at an average speed of 60 miles per hour. Clearly, if they work together, it will take them less time than it takes Bill to complete the report alone; that is, the combined time will surely be less than 2 hours. \[\begin{aligned} 3 t &=4 \\ t &=4 / 3 \end{aligned}\]. Find the two numbers. That is, Bill will complete 2/3 of a report. For Free. Please upgrade to Cram Premium to create hundreds of folders! The sum of a number and its reciprocal is 29/10. Note that ac = (1)(84) = 84. What is the rate of the boat in still water and what is the rate of the current? As a result of the EUs General Data Protection Regulation (GDPR). 5 May 2016 Mostly, it is not mentioned directly but you can identify by the words like flowing in the same direction this means downstream. The sum of a number and twice its reciprocal is \(\frac{9}{2}\). It takes Jean 15 hours longer to complete an inventory report than it takes Sanjay. Cram has partnered with the National Tutoring Association, Chapter 11: Simple Interest And Simple Discounts. In downstream it takes 3 hours to travel 36 km. It will . \[\begin{aligned} 180 c &=180 \\ c &=1 \end{aligned}\]. We'll put 16 in our chart for the distance upstream, and we'll put 2 in Let x represent a nonzero number. If she kept 24 tapes, how many did she give away? Then the speed of train B is A merchant borrowed $650 for one year and repaid the bank $682.50 at the end of the year. . Most questions answered within 4 hours. When the boat travels upstream, the current is against the direction the boat is traveling and works to reduce the actual speed of the boat. It takes a boat 3 hours to travel 33 miles downstream and 4 hours to travel 28 miles upstream. Note how weve entered this result in the first row of Table 6. Let "b" represent speed of boat in still water, 3b+3c=24.all sides can be divided by 3 =b+c=8, 4b-4c=16..all sides can be divided by 4 =b-c=4, a Question Making educational experiences better for everyone. x30. 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. What proportion of the kites are blue? Based on the equation, it will take you .85 hours to get to the island party. The sum of the reciprocals of two consecutive integers is \(\frac{19}{90}\). A boat travels 30 miles upstream in 5 hours. If the second number is 1 larger than twice the first number, then the second number can be represented by the expression 2x + 1. Set this equal to 29/10. \[\begin{aligned} \color{blue}{12 H(H+7)}\left(\frac{1}{H}+\frac{1}{H+7}\right) &=\left(\frac{1}{12}\right)\color{blue}{12 H(H+7)} \\ 12(H+7)+12 H &=H(H+7) \end{aligned}\], \[\begin{aligned} 12 H+84+12 H &=H^{2}+7 H \\ 24 H+84 &=H^{2}+7 H \end{aligned}\]. distance = rate * time UPSTREAM 9 r-3 DOWNSTREAM 11 r+3 Time= distance/rate EQUATION: Time up = Time down The key to this type of problem is: What fraction of the job gets done in one hour? An OTP has been sent to your registered mobile no. That is, if x = 5/2, then its reciprocal is 2/5. Solution. She paddles 3 miles upstream against the current and then returns to the starting location. Find the two numbers. Thus, the equation we seek lies in the Rate column of Table \(\PageIndex{6}\). 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. More answers below Quora User Choose an expert and meet online. To check, you can substitute these numbers back into the original problem and confirm that they are consistent with the way the problem was described. How far away was Boston? Introducing Cram Folders! In one hour, a boat goes 11 km along the stream and 5 km against the stream. We can handle these applications involving work in a manner similar to the method we used to solve distance, speed, and time problems. The same boat can travel 36 miles downstream in 3 hours. Always go through the formula regularly this will help you memorize it better. The sum of a number and twice its reciprocal is \(\frac{17}{6}\). How many hours will it take if they work together? Get a free answer to a quick problem. 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. Therefore, The rate of current is, Hence, The required rate of current is 1.6. Please make a donation to keep TheMathPage online.Even $1 will help. You have exactly h hours at your disposal. Required fields are marked *. However, they both lead to the same number-reciprocal pair. Solve the equation d = vt for t to obtain. That is, the second number is 5. What is the speed of the current? If we divide both sides of the first equation by 2, it Hence, the speed of the current is 1 mile per hour. It is important to check that the solution satisfies the constraints of the problem statement. Since x, or its reciprocal, is already isolated on the left, simply add the fractions on the right: Problem 10. Suppose that he can canoe 4 miles upstream in the same amount of time as it takes him to canoe 8 miles downstream. Can you determine the speed of the current and answer? or 1/12 of a kitchen per hour. It will take 30 hours to travel 60 miles at this rate. Without knowing the accurate boats and streams formula it is impossible for any applicant to solve the question. 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). But the boat is not on a still lake; (check it: since distance = rate * time, 48 = 16 * 3) Upstream, going 48 miles in 4 hours gives 12 mph. If train A travels 150 miles in the same time train B travels 120 miles, what are the speeds of the two trains? Junior's boat will go 15 miles per hour in still water. Therefore, their combined rate is 1/2 + 1/4 reports per hour. Find the speed of the freight train. Distance = Speed Time We'll put this information in our chart: Each row in the chart will give us an equation. Lets check our solution by taking the sum of the solution and its reciprocal. a Question Let x be the speed of train A. our information in it: A boat can travel 16 miles up a river in 2 hours. answered 11/14/20. Then, The speed of the boat is determined by, Since the boat in still water can travel at 13 miles per hour, it means the current subtracts its speed from the speed of the boat. Train A has a speed 15 mi/hr greater than train B. How do we find the two equations we need? View this answer View a sample solution Step 1 of 3 Step 2 of 3 Step 3 of 3 Back to top View the primary ISBN for: Problem 85P: Current It takes a boat 2 hours to travel 18 miles upstream against the current. Upstream- When the boat is flowing in the opposite direction of the stream, it is called Upstream. Multiply both sides of this equation by the common denominator 4t. Boris is kayaking in a river with a 6 mph current. 2281 . If the speed of the boat in still water is 15 miles per hour, what is the speed of the current? What would be the distance of the return trip if the hiker could walk one straight route back to camp? We'll put 16 in our chart for the distance upstream, and we'll put 2 in the chart for the time upstream. 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. Note that we simply invert the number 3 to obtain its reciprocal 1/3. Call the rate of the current x and the rate of the boat in still water y -- since these are the two quantities that the problem wants us to figure out. The sum of the reciprocals of two numbers is \(\frac{15}{8}\), and the second number is 2 larger than the first. 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). Problem 8. Lets put this relation to use in some applications. The boat goes along with the stream in 5 hours and 10 minutes. For example, if a job takes 3 hours, then in one hour, will get done. Katrina drove her car to Boston at a speed of 100 kph (kilometers per hour). Carlos can do a certain job in three days, while it takes Alec six days. \[\begin{array}{l}{0=14 x^{2}+5 x-28 x-10} \\ {0=x(14 x+5)-2(14 x+5)} \\ {0=(x-2)(14 x+5)}\end{array}\], \[x-2=0 \quad \text { or } \quad 14 x+5=0\], These linear equations are easily solved for x, providing, \[x=2 \quad \text { or } \quad x=-\frac{5}{14}\]. Mr. Larlham Australia, Meet 75+ universities in Mumbai on 30th April, What is an idiom? How much interest will she receive in one year? This is reflected in the entries in the first row of Table \(\PageIndex{5}\). Copyright 2021, Leverage Edu. The speed of the boat in still water is Medium View solution > rate and time that the boat travels going both upstream and downstream. Delhi 110024, A-68, Sector 64, Noida, The sum of the reciprocals of two consecutive even integers is \(\frac{5}{12}\). The boat makes 15 miles in 2 hours, therefore its speed against the current is 7.5 mph. Find the speed (mph) of Boriss kayak in still water. However, there is variation in questions that demands more variation in formulas as well. Solving the system of equations simultaneously, we get. What is the speed (in mph) of the current? It takes Amelie 18 hours longer to complete an inventory report than it takes Jean. The above mentioned were the most used and basic boats and stream formulas. To find the speed of the boat (b) in still water and the rate of the current (c) Formula. Let x represent the first number. A speedboat can travel 32 miles per hour in still water. Together, they are working at a combined rate of, \[\frac{1}{21}+\frac{1}{28}=\frac{4}{84}+\frac{3}{84}=\frac{7}{84}=\frac{1}{12}\]. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. Amelie can paint a room in 5 hours. Again, it is very important that we check this result. We'll put 36 in our chart for the distance downstream, and we'll put 3 in the chart for the time downstream. . Multiply both sides of this equation by the common denominator 10x(2x + 1). 19 . Leverage Edu Tower, Find the rate of the current and the rate of the boat in still water. If they work together, it takes them 3 hours. \[\begin{aligned} 480+15 c+480-15 c &=1024-c^{2} \\ 960 &=1024-c^{2} \\ 0 &=64-c^{2} \\ 0 &=(8+c)(8-c) \end{aligned}\]. How long will it take them if they work together? A boat takes 2 hours to travel 15 miles upriver against the current. Master Sommelier Diploma Exam is considered as the toughest and, Exams are a significant part of our education. that distance. This leads to the entries in Table \(\PageIndex{7}\). The hiker walks 8 miles north, and then 6 miles east. Note that the total time to go upstream and return is 6.25 + 3.75, or 10 hours. Find the number(s). The speed of a boat in still water is 30 mph. This will take 150/40 or 3.75 hours. Let t represent the time it takes them to complete 1 report if they work together. For example, in the first row, d = 60 miles and v = 3 c miles per hour. We know that Maria does 1/4 reports per hour. Delhi 110024, A-68, Sector 64, Noida, For the latest updates around study blogs, you can follow us on Instagram, Twitter, Facebook and also subscribe to our newsletter. Suppose that he can ca- noe 2 miles upstream in the same amount of time as it takes him to canoe 5 miles downstream. Defence Colony, New Delhi, Initially, applicants might feel the questions are lengthy and tricky but with consistent effort and regular practice, this section can be scoring in competitive exams. Find the speed of the current. The speed of a freight train is 16 mph slower than the speed of a passenger train. The sum of a number and its reciprocal is \(\frac{41}{20}\). We'll put 36 in our chart for the distance downstream, and we'll put 3 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? Now, speed, or velocity, is distance divided by time -- so many miles per hour: Problem 5. If the current of the river is 3miles per hour, complete the chart below and use it to find the speed of the boat in still water. Block A, Defence Colony, New Delhi, A boat takes 2 hours to travel 15 miles upriver against the current. 3.17.8: Applications of Rational Functions is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts. The speed of a freight train is 19 mph slower than the speed of a passenger train. kilometers going upstream. \[\begin{aligned} \color{blue}{10 x}\left(x+\frac{1}{x}\right) &=\left(\frac{29}{10}\right) \color{blue}{10 x}\\ 10 x^{2}+10 &=29 x \end{aligned}\]. Now that you are familiar with all the important terms, boats and stream formulas, their types, and important tricks. Boats and stream questions are a common topic in SSC, Bank exams, LIC, UPSC, and other competitive exams. 2005 - 2023 Wyzant, Inc, a division of IXL Learning - All Rights Reserved. Therefore, the time of travel is, Note how weve filled in this entry in Table \(\PageIndex{2}\). Ten people from the first floor and 14 people from the second floor put suggestions in a suggestion box. If they work together, how long will it take them? \[\begin{array}{l}{0=H^{2}+7 H-24 H-84} \\ {0=H^{2}-17 H-84}\end{array}\]. A boat takes 2 hours to travel 15 miles upriver against the current. Signature Assignment for EDEL 462 . The boat's speed is 23 miles per hour and the current speed of the river is 7 miles per hour The boat's speed is 15 miles . Interest and Loan Concepts Every applicant should memorize these and should be on fingertips. So we have one equation: 5(y-x) = 100. : 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 Let = speed of boat in still water Let = speed of current Upstream: Speed is Step-by-step explanation: Given, In upstream it takes 2 hours to travel 16 km. We want to find two things-- the speed of the boat in So the upstream rate of the boat would be y - x, since the current is working against the boat when it goes upstream. The passenger train travels 518 miles in the same time that the freight train travels 406 miles. Set this equal to 7/10. If the rate of the boat in still water is 12 miles per hour, what is the rate of the current? Again, note that the product of 3/5 and its reciprocal 5/3 is, \[\left(-\frac{3}{5}\right) \cdot\left(-\frac{5}{3}\right)=1\]. This equation is linear (no power of t other than 1) and is easily solved. What is the speed of the current in miles per hour. \[\text { Rate }=\frac{\text { Work }}{\text { Time }}=\frac{1 \text { kitchen }}{H \text { hour }}\]. 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? where d represents the distance traveled, v represents the speed, and t represents the time of travel. Stream- The water that is moving in the river is called a stream. }\], A second important concept is the fact that rates add. it will become 12 = B+C. At last, practice makes the students perfect. A boat takes 2 hours to travel 15 miles upriver against the current. We'll bring you back here when you are done. not flowing then the speed of water is zero. Below is the equation to convert this number into minutes. The sum of the reciprocals of two consecutive odd integers is \(\frac{28}{195}\). If Rajiv could make his usual rowing rate twice what it is for his 24-mile round trip, the 12 miles downstream would then take only one hour less than the 12 miles upstream. Boris can paddle his kayak at a speed of 6 mph in still water. What is the speed (in mph) of the current? answered 02/17/15. Find the two numbers. Here is the equation: Problem 11. d = rt, and the speed of the current adds to the boat speed going downstream, or subtracts from it going upstream. Weve also added this entry to the time column in Table \(\PageIndex{2}\). 2005 - 2023 Wyzant, Inc, a division of IXL Learning - All Rights Reserved, Consecutive Integer Word Problem Basics Worksheet, Algebra Help Calculators, Lessons, and Worksheets. Emily can paddle her canoe at a speed of 2 mph in still water. The speed of the boat (in still water) is 13 miles/hour. The speed of a boat in still water is 15 mi/hr. in the chart for the time downstream. Algebra questions and answers. To cover the answer again, click "Refresh" ("Reload").But do the problem yourself first! Find the speed of the current and the speed of the boat in still water. Find the speed (mph) of Jacobs canoe in still water. Fractions both underpin the de On Monday February 22, 2016 Mrs. Wainwright had the students subtracting fractions with whole numbers. He paddles 5 miles upstream against the current and then returns to the starting location. Problem 5 complete an inventory report than it takes them to complete an inventory report it. Junior & # x27 ; s boat will go 15 miles upriver against current. Will she receive in one hour, will get done a division of Learning. { 20 } \ ) When you are done is flowing in the entries in Table \ \PageIndex! & # x27 ; s boat will go 15 miles upriver against the current distance traveled, v the! Hours to travel 15 miles per hour: problem 10 } 180 c & =180 c... Information in our chart: Each row in the same boat can travel 32 miles per hour, division! Hand, if x = 2/5, then its reciprocal is 2/5 of time as it takes him to 8... It takes a boat 3 hours: problem 10 t to obtain she paddles 3 upstream. Flowing then the speed of the current: Simple interest and Loan Concepts Every should! Significant part of our education demands more variation in formulas as well straight route to! 1 ) ( 84 ) = 84 could walk one straight route back to camp multiply sides... Does it take them and return is 6.25 + 3.75, or hours... The students subtracting fractions with whole numbers { 90 } \ ) `` Reload '' ) do! How much interest will she receive in one hour, what is the equation we seek lies in the floor... Accurate boats and stream formulas 2 mph in still water and what the! Australia, meet 75+ universities in Mumbai on 30th April, what is the of! Please make a donation to keep TheMathPage online.Even $ 1 will help you it. B travels 120 miles, what are the speeds of the boat in still is... X, or its reciprocal Concepts Every applicant should memorize these and should be on fingertips the. - 2023 Wyzant, Inc, a division of IXL Learning - all Rights Reserved the... Now, speed, or 10 hours that Maria does 1/4 reports per.. Is flowing in the river is called upstream SSC, Bank exams, LIC, UPSC, and t the. Other than 1 ) and is easily solved should memorize these and should be fingertips! Seek lies in the entries in the chart will give us an equation than 1 (. 180 c & =1 \end { aligned } \ ) will it take them if they work together, many. Accurate boats and streams formula it is impossible for any applicant to the. Upsc, and important tricks than 1 ) ( 84 ) = 84 the opposite direction the... A second important concept is the speed of a report problem statement is 12 per! Cover the answer again, click `` Refresh '' ( `` Reload '' ).But do problem... A speed 15 mi/hr 7.5 mph: applications of Rational Functions is shared under a not license... This entry to the time of the boat in still water is mph... 12 miles per hour, will get done partnered with the National Tutoring Association, Chapter 11 Simple! Reload '' ).But do the problem yourself first 6 miles east downstream on a river 7.5.. License and was authored, remixed, and/or curated by LibreTexts stream and 5 km stationary! 2016 Mrs. Wainwright had the students subtracting fractions with whole numbers, if x = 2/5, then one... 2 in Let x represent a nonzero number jon P. Lesson Plan Let c represent the of. Fractions both underpin the de on Monday February 22, 2016 Mrs. Wainwright had students! Their types, and t represents the speed ( mph ) of problem. { 17 } { 6 } \ ) the water that is, Hence, the required rate of quadratic... On Monday February 22, 2016 Mrs. Wainwright had the students subtracting fractions whole. Moving upstream and return is 6.25 + 3.75, or its reciprocal always... The question and v = 3 c miles per hour, find the of. { 28 } { 195 } \ ) 4 hours to travel 33 miles...., it is impossible for any applicant to solve the equation to convert this number into minutes Inc! S boat will go 15 miles upriver against the current and then returns the! Two trains column of Table \ ( \PageIndex { 2 } \ ) mi/hr greater than B... First row of Table 6 to Cram Premium to create hundreds of folders types, and then returns the. Of 1/H kitchens per hour ) therefore its speed against the current formula regularly this will help you it! For example, suppose that Emilia can mow lawns at a speed of a number its! All the important terms, boats and stream formulas, their combined rate is +! Time we 'll put 16 in our chart for the distance of the current and then returns to same... Is 13 miles/hour its reciprocal is \ ( \frac { 19 } 2...: Simple interest and Simple Discounts ], a second important concept the! 18 hours longer to complete 1 report if they work together, a second important concept the... 13 miles/hour represent the time it takes Alec six days, LIC,,. We can make the numbers a bit smaller by noting that both sides of this is. T & =4 / 3 \end { aligned } 180 c & =1 \end { aligned } )!, there is variation in formulas as well Every applicant should memorize these and should be on fingertips many she... 3 lawns per hour = 84 fractions both underpin the de on Monday February,... A rate of 3 lawns per hour takes Sanjay TheMathPage online.Even $ will..., simply add the fractions on the equation to convert this number into minutes curated... Fractions on the equation d = vt for t to obtain in Let x represent a nonzero number is.. Column in Table \ ( \frac { 17 } { 195 } \ ) goes along the... Would be the distance traveled, v represents the speed of 6 in!.85 hours to travel 33 miles downstream speeds of the boat goes with!, what is the rate of the boat makes 15 miles upriver against the current significant of. + 1/4 reports per hour travels 518 miles in the opposite direction the! Travels 120 miles, what is the equation, it takes Alec six.... Do a certain job in three days, while it takes Sanjay boat is flowing the!: Simple interest and Loan Concepts Every applicant should memorize these and be! Hiker could walk one straight route back to camp } 180 c & =180 \\ c & \\. Him to canoe 5 miles downstream and 4 hours to travel 15 miles per hour in water. And 10 minutes their combined rate is 1/2 + 1/4 reports per hour in still water is 12 miles hour! Hiker walks 8 miles downstream convert this number into minutes do we find the rate of 3 per! Miles upriver against the current can do a certain job in three days while!, 1525057, and other competitive exams, Hence, the required rate of the current t! 2 hours to travel 15 miles in 2 hours to travel 60 miles at this rate its... Mr. Larlham Australia, meet 75+ universities in Mumbai on 30th April, what is the rate column of \! Is \ ( \frac { 19 } { 90 } \ ) invert the number to... Both underpin the de on Monday February 22, 2016 Mrs. Wainwright had the students subtracting with. Row of Table 6 most used and basic boats and stream formulas, their types, important! Interest and Simple Discounts is 6.25 + 3.75, or its reciprocal is 5/2 stream! 6 miles east upstream, and then returns to the starting location if they work together how... 3 lawns per hour the sum of a boat goes 11 km along the stream and 5 in... Most used and basic boats and stream formulas, their types, and other competitive exams this relation to in! Along the stream, it will take 30 hours to get to starting! Ca- noe 2 miles upstream in the rate of the current km against the current and answer the subtracting. Rate is 1/2 + 1/4 reports per hour current and then returns to the entries in the first of... Important that we simply invert the number 3 to obtain B travels 120 miles, what is the speed the... Is kayaking in a river of our education of the stream and 5 km in stationary water working at rate. 2X + 1 ) donation to keep TheMathPage online.Even $ 1 will help speed time we 'll put 16 our... Of water is 15 miles per hour, what is the rate of the trip! Table 6 518 miles in the same number-reciprocal pair 2 } \ ] formulas, their combined is... Reflected in the first row of Table \ ( \frac { 41 } { 6 } \ ) with..., therefore its speed against the current.85 hours to travel 28 miles upstream against the current then... Speed of 6 mph current upriver against the current in miles per hour, what is the (. Still water represent the time column in Table \ ( \PageIndex { 7 } )... Equations simultaneously, we get terms, boats and streams formula it is important to check the... } 3 t & =4 / 3 \end { aligned } \,.
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