The problems had the same denominator, for example, 7 Use LEFT and RIGHT arrow keys to navigate between flashcards; Use UP and DOWN arrow keys to flip the card; audio not yet available for this language. If the rate of the boat in still water is 13 miles per hour what is the rate of the - 20218675 2003-2023 Chegg Inc. All rights reserved. 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? 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 Expand and simplify each side of this result. Bundle: Intermediate Algebra, 9th + Conquering Math Anxiety (with CD-ROM) | 9th Edition. Introducing Cram Folders! A boat can travel 24 miles in 3 hours when traveling with a current. She paddles 5 miles upstream against the current and then returns to the starting location. Our chart now looks like . Raymond can do a job in 3 hours, while it takes Robert 2 hours. Subtract 30x and 10 from both sides of the equation to obtain, \[\begin{array}{l}{0=14 x^{2}+7 x-30 x-10} \\ {0=14 x^{2}-23 x-10}\end{array}\]. 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 \(\PageIndex{7}\). On a map, 2.5 inches represents 300 miles. Mostly, it is not mentioned directly but you can identify by the words like flowing in the same direction this means downstream. He started at the tower's base and is now 35 feet above the ground. Maria can finish the same report in 4 hours. Going downstream, it can travel 60 miles in the same amount of time. If they work together, how long will it take them? it's moving upstream and downstream on a river. How long does it take Hank to complete the job if he works alone? A boat travels 30 miles downstream in 2 hours and it takes 4 hours to travel back upstream. Let = speed of boat in still water Let = speed of current Upstream: Speed is Then. 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). 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. Australia, Leverage Edu Tower, Problem 6. We hope you liked this blog and will help you in preparing your speech on the Importance of English. answered 11/14/20, Mathematics Teacher - NCLB Highly Qualified. Let's see what kinds of equations we can come up with. The length of a flag is 1.9 times its width. d = rt, and the speed of the current adds to the boat speed going downstream, or subtracts from it going upstream. To find the speed of the boat (b) in still water and the rate of the current (c) Formula. First, let us explain the meaning of "upstream" and "downstream.". Add to folder The sum of a number and twice its reciprocal is \(\frac{9}{2}\). Solution. The sum of the reciprocals of two consecutive even integers is \(\frac{5}{12}\). Again, it is very important that we check this result. Katrina drove her car to Boston at a speed of 100 kph (kilometers per hour). \[\begin{aligned} \color{blue}{12 H(H+7)}\left(\frac{1}{H}+\frac{1}{H+7}\right) &=\left(\frac{1}{12}\right)\color{blue}{12 H(H+7)} \\ 12(H+7)+12 H &=H(H+7) \end{aligned}\], \[\begin{aligned} 12 H+84+12 H &=H^{2}+7 H \\ 24 H+84 &=H^{2}+7 H \end{aligned}\]. 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. The speed of the boat as it goes downstream (with the current) will be 4 miles per hour. A common misconception is that the times add in this case. Break up the middle term of the quadratic trinomial using this pair, then factor by grouping. Hence, the speed of the current is 1 mile per hour. Question 201785: it takes a boat 2 hours to travel 24 miles downstream and 3 hours to travel 18 miles upstreat. Against the same current, it can travel only 16 miles in 4 hours. We'll bring you back here when you are done. In still water, your small boat average 8 miles per hour. This problem ask the students to use division to solve the problem and they were not able to do that. We can handle these applications involving work in a manner similar to the method we used to solve distance, speed, and time problems. We'll put 36 in our chart for the distance downstream, and we'll put 3 in the chart for the time downstream. What are the speed of the boat in still water and the speed of the stream? 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 Answer: 1 hour 15 minutes. 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. Multiple Subject Credential Program That is, the second number is 5. How many hours will it take if they work together? 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. Please verify. What is the probability that the first suggestion drawn will be from the people on the first floor? If she kept 24 tapes, how many did she give away? That is, \[a \cdot \frac{1}{a}=1\], For example, the reciprocal of the number 3 is 1/3. Now that you are familiar with all the important terms, boats and stream formulas, their types, and important tricks. This equation is linear (no power of t other than 1) and is easily solved. {\(\frac{2}{3}\), \(\frac{8}{3}\)} and {\(\frac{8}{5}\), \(\frac{2}{5}\)}. The total time of the trip is 9 hours. 5600 = ___________________ Expand, simplify, make one side zero, then factor. Defence Colony, New Delhi, }\]. 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. Get a free answer to a quick problem. Clearly, working together, Bill and Maria will complete 2/3 + 1/3 reports, that is, one full report. Choose an expert and meet online. Find the speed (mph) of Jacobs canoe in still water. A boat takes 1.5 hour to go 12 mile upstream against the current. Solution. What was the average speed during the whole journey? Therefore, their combined rate is 1/2 + 1/4 reports per hour. Let x be that time. Introducing Cram Folders! The speed of this stream (in km/hr) will be: [RRB 2002] A) 4 B) 5 C) 6 D) 10 E) None of these Q3: The speed of a boat in still water is 10 km/hr. We can make the numbers a bit smaller by noting that both sides of the last equation are divisible by 10. It takes Amelie 18 hours longer to complete an inventory report than it takes Jean. Australia, Meet 75+ universities in Mumbai on 30th April, What is an idiom? 2(b + c) = 128. b - c = 32. b . A-258, Bhishma Pitamah Marg, Block A, Jean can paint a room in 4 hours. If they work together, it takes them 3 hours. If the speed of the boat in still water is 15 miles per hour, what is the speed of the current? For in one hour, Raymond does of the job, and Robert, . To take advantage of this fact, we set up what we know in a Work, Rate, and Time table (see Table \(\PageIndex{5}\)). Step-by-step solution Chapter 2.2, Problem 85P is solved. Find the two numbers. To find the speed of the current, we can substitute 10 a Question We want to find two things-- the speed of the boat in Hence, \[H+4=0 \quad \text { or } \quad H-21=0\]. Please upgrade to Cram Premium to create hundreds of folders! The speed of a freight train is 16 mph slower than the speed of a passenger train. Going up stream 5 miles at speed relative to shore of 8-4 = 4 mph takes 1.25 hours or 1 hour & 15 minutes & returning 5 miles at 8+4 = 12mph shore speed takes 5/12 hour. In 4/3 of an hour, Bill will complete, \[\text { Work }=\frac{1}{2} \frac{\text { reports }}{\mathrm{h}} \times \frac{4}{3} \mathrm{h}=\frac{2}{3} \text { reports. Find the two numbers. \[\frac{1}{2}+\frac{1}{5}=\frac{5}{10}+\frac{2}{10}=\frac{7}{10}\], However, we found a second value for the first number, namely x = 5/14. Upstream- When the boat is flowing in the opposite direction of the stream, it is called Upstream. Also Read: A Guide On How to Prepare for Bank Exams. To see the equation, pass your mouse over the colored area. for the B in any of our equations. Water volume increases 9% when it freezes. Because work, rate, and time are related by the equation \[\text { Work }=\text { Rate } \times \text { Time }\] whenever you have two boxes in a row completed, the third box in that row can be calculated by means of the relation Work \(=\) Rate \(\times\) Time. For Free. As a result of the EUs General Data Protection Regulation (GDPR). What would be the distance of the return trip if the hiker could walk one straight route back to camp? 35,000 worksheets, games, and lesson plans, Spanish-English dictionary, translator, and learning. Krishan W. Thus, Bill is working at a rate of 1/2 report per hour. Let's say I'm in a 10 mph current in a canoe. The speed of a boat in still water is 15 mi/hr. 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. Downstream- When the boat is flowing in the same direction as the stream, it is called Downstream. How far away was Boston? 35,000 worksheets, games, and lesson plans, Spanish-English dictionary, translator, and learning, a Question Answer by josmiceli (19441) ( Show Source ): You can put this solution on YOUR website! Lets look at some applications that involve the reciprocals of numbers. Next Lesson: Radicals: Rational and irrational numbers. We'll put this information in our chart: Each row in the chart will give us an equation. Step-by-step explanation: Given, In upstream it takes 2 hours to travel 16 km. 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. In one hour, a boat goes 11 km along the stream and 5 km against the stream. What is the speed of the boat if it were in still water and what is the speed of the river current? View this answer View a sample solution Step 1 of 3 Step 2 of 3 Step 3 of 3 Back to top 2005 - 2023 Wyzant, Inc, a division of IXL Learning - All Rights Reserved. Lets try to use the ac-test to factor. The passenger train travels 518 miles in the same time that the freight train travels 406 miles. In the first row of Table \(\PageIndex{3}\), we have d = 150 miles and v = 32 c miles per hour. \[\frac{1}{H}+\frac{1}{H+7}=\frac{1}{12}\]. When a boat travels in the same direction as the current, we say that it is traveling downstream. Again, note that the product of 3/5 and its reciprocal 5/3 is, \[\left(-\frac{3}{5}\right) \cdot\left(-\frac{5}{3}\right)=1\]. 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. Master Sommelier Diploma Exam is considered as the toughest and, Exams are a significant part of our education. That is, together they work at a rate of 1/t reports per hour. Going downstream, Distance = (Rate)(Time), so 36 = (B+C)(3). 1] . Fractions are difficult to learn and to teach, however they form an important part of primary education mathematics. For example, suppose that Emilia can mow lawns at a rate of 3 lawns per hour. The speed of the boat in still water is 3 miles per hour. However, the last row of Table \(\PageIndex{6}\) indicates that the combined rate is also 1/t reports per hour. A nice application of rational functions involves the amount of work a person (or team of persons) can do in a certain amount of time. A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. A woman deposits $600 into an account that pays 5 1/4 interest per year. Freshwater, Sydney, NSW 2096, If we divide both sides of the second equation by 3, A boat travels 24 km upstream in 6 hours and 20 km downstream in 4 hours. It takes you the same amount of time to travel 15 miles downstream, with the current, as 9 miles upstream, against the current. Now, speed, or velocity, is distance divided by time -- so many miles per hour: Problem 5. Find the speed of the current and the speed of the boat in still water. Solution. A-258, Bhishma Pitamah Marg, That will give the equation, Time upstream = Time downstream Now, speed, or velocity, is distance divided by time -- so many miles per hour: Therefore, t = d v The equation will be Problem 5. The third entry in each row is time. whereas when traveling upstream it is 28 km/hr. Each of these linear equations is easily solved. distance = rate * time UPSTREAM 9 r-3 DOWNSTREAM 11 r+3 Time= distance/rate EQUATION: Time up = Time down A boat travels a distance of 80 km in 4 hours upstream and same distance down stream in 2 hours in a river. A merchant borrowed $650 for one year and repaid the bank $682.50 at the end of the year. Note that the time to travel upstream (30 hours) is twice the time to travel downstream (15 hours), so our solution is correct. Here is the guiding principle. the speed of the boat in still water? You will only be able to solve these questions if you have memorized the boats and streams formula. What was the interest rate on the loan? He paddles 5 miles upstream against the current and then returns to the starting location. The last part of the equation is to subtract the travel time by boat from the time the party starts. The key to this type of problem is same time . Note that each row of Table \(\PageIndex{1}\) has two entries entered. To clear fractions from this equation, multiply both sides by the common denominator 10x. On the other hand, if x = 2/5, then its reciprocal is 5/2. He calculated the speed of the river that day as 1 km/hr. A boat takes 1.5 hour to go 12 mile upstream against the current. A boat takes 2 hours to travel 15 miles upriver against the current. Jon P. 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? Find the speed of the freight train. What proportion of the kites are blue? \[\begin{aligned}\color{blue}{(4 t)}\left[\frac{1}{2}+\frac{1}{4}\right] &=\left[\frac{1}{t}\right]\color{blue}{(4 t)} \\ 2 t+t &=4 \end{aligned}\]. Choose an expert and meet online. Your contact details will not be published. So we have one equation: 5(y-x) = 100. Note how weve entered this result in the first row of Table 6. Let x be the speed of train A. . Find the speed of the freight train. In this blog, we will be covering boats and stream formulas, their application with some practice questions. 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? 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. Best Answer #1 +118288 +10 . Making educational experiences better for everyone. . An OTP has been sent to your registered mobile no. If he can paddle 5 miles upstream in the same amount of time as it takes his to paddle 9 miles downstream, what is the speed of the current? We still need to answer the question, which was to find two numbers such that the sum of their reciprocals is 7/10. Stream- The water that is moving in the river is called a stream. Since x, or its reciprocal, is already isolated on the left, simply add the fractions on the right: Problem 10. Let x = will become 8 = B-C. A train travels 30 mi/hr faster than a car. The speed of the current is miles per hour. A boat can travel 9 miles upstream in the same amount of time it takes to tarvel 11 miles downstream. However, as we saw above, the rates at which they are working will add. A boat takes 2 hours to travel 15 miles upriver against the current. If train A travels 150 miles in the same time train B travels 120 miles, what are the speeds of the two trains? How many miles are represented by 6 inches? so we have 2 equations which must be solved . per hour. If 180 cubic centimeters of water is frozen, by how many cubic centimeters will its volume increase? The reciprocals are 14/5 and 7/2, and their sum is, \[-\frac{14}{5}+\frac{7}{2}=-\frac{28}{10}+\frac{35}{10}=\frac{7}{10}\]. 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. be represented by a different variable: Since we have two variables, we will need to find a system A painter can paint 4 walls per hour. \[\begin{aligned} 480+15 c+480-15 c &=1024-c^{2} \\ 960 &=1024-c^{2} \\ 0 &=64-c^{2} \\ 0 &=(8+c)(8-c) \end{aligned}\]. It will take 30 hours to travel 60 miles at this rate. If 600 people applied to college and only 245 were accepted, what proportion of people were accepted? This leads to the result, \[\frac{60}{3-c}=2\left(\frac{60}{3+c}\right)\]. We'll put 16 in our chart for the distance upstream, and we'll put 2 in . Sanjay can paint a room in 5 hours. Example 4. Their reciprocals, respectively, are 1/x and 1/(2x + 1). How do we find the two equations we need? 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? It takes Jean 15 hours longer to complete an inventory report than it takes Sanjay. Find the speed of the current and the speed of the boat in still water. The boat goes along with the stream in 5 hours and 10 minutes. But the boat is not on a still lake; to work with: The speed of the current is 2 miles per hour. . The trip each way is 150 miles. It takes Bill 2 hours to complete 1 report. Round your answer to the nearest hundredth. You have exactly h hours at your disposal. The sum of a number and its reciprocal is 29/10. 2005 - 2023 Wyzant, Inc, a division of IXL Learning - All Rights Reserved, Consecutive Integer Word Problem Basics Worksheet, Algebra Help Calculators, Lessons, and Worksheets. 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. 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. When a boat travels against the current, it travels upstream. The integer pair {4, 25} has product 100 and sum 29. Lesson Title: The current speed . This will take 150/40 or 3.75 hours. We eliminate the solution H = 4 from consideration (it doesnt take Hank negative time to paint the kitchen), so we conclude that it takes Hank 21 hours to paint the kitchen. \[Rate \(=\frac{\text { Work }}{\text { Time }}=\frac{1 \text { report }}{t \mathrm{h}}\)\]. United Kingdom, EC1M 7AD, Leverage Edu 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. Please sign in to share these flashcards. When traveling downstream speed = boat + current = 20miles in 2 hours = 10miles/hour. In downstream it takes 3 hours to travel 36 km. not flowing then the speed of water is zero. How much interest will she receive in one year? Two people working together can complete a job in six hours. Block A, Defence Colony, New Delhi, How many hours will it take if they work together? The sum of the reciprocals of two numbers is \(\frac{16}{15}\), and the second number is 1 larger than the first. Round your answer to the nearest hundredth. This is an alternate ISBN. This is reflected in the entries in the last row of Table \(\PageIndex{5}\). It takes Sanjay 7 hours to paint the same room. This was all about the Boats and streams formula. How many hours would it take Sanjay if he worked alone? Together, they can complete the same job in 12 hours. It takes Amelie 9 hours to paint the same room. Here is the equation: Problem 11. Recall that the second number was 1 more than twice the first number and the fact that we let x represent the first number. then the time taken by the boat to travel 100 km with the current is? Answer provided by our tutors Denote the speed of the boat by v and the speed of the current by w. David W. Example 3. We know that if the boat were on a still lake, its motor would propel it A merchant borrowed $650 for one year and repaid the bank $682.50 at the end of the year. Going upstream, Distance = (Rate)(Time), so 16 = (B-C)(2) Find the speed (mph) of Jacobs canoe in still water. The speed of a boat in still water is 30 mph. The hiker walks 8 miles north, and then 6 miles east. Solution. It is important to check that the solution satisfies the constraints of the problem statement. 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. Mr. Larlham that distance. That is, \[\text { Work }=\text { Rate } \times \text { Time. It takes Maria 4 hours to complete 1 report. The speed of the boat in still water is Medium View solution > This leads to the entries in Table \(\PageIndex{7}\). It travels 150 miles upstream against the current then returns to the starting location. Find the speed of the current and the speed of the boat in still water. Jacob can paddle his kayak at a speed of 6 mph in still water. 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. To organize our work, we'll make a chart of the distance, The total time of the trip is 10 hours. The return trip takes2. hours going downstream. Consequently, if the first number is x = 2, then the second number is 2x + 1, or 2(2) + 1. The key to this type of problem is same time. Let x represent the first number. A link to the app was sent to your phone. If the speed of the boat in still water is 15 miles per hour, what is the speed of the current? Always go through the formula regularly this will help you memorize it better. Each of these things will Together, they are working at a combined rate of, \[\frac{1}{21}+\frac{1}{28}=\frac{4}{84}+\frac{3}{84}=\frac{7}{84}=\frac{1}{12}\]. A boat can travel 24 miles in 3 hours when traveling with a current. We'll put 36 in our chart for the distance downstream, and we'll put 3 How tall is the tower? 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. 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? \[x=\frac{5}{2} \quad \text { or } \quad x=\frac{2}{5}\]. The speed of a freight train is 20 mph slower than the speed of a passenger train. She paddles 3 miles upstream against the current and then returns to the starting location. Emily can paddle her canoe at a speed of 2 mph in still water. 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. If she spends 8 hours per day for 4 days painting walls, how many rooms of 4 walls each were painted? Let x represent a nonzero number. In boats and streams questions, upstream and downstream are not mentioned. 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. To set up an equation, we need to use the fact that the time to travel upstream is twice the time to travel downstream. Going upstream, the boat struggles against the current, so its net speed is 32c miles per hour. After 6 hours, \[\text { Work }=3 \frac{\text { lawns }}{\mathrm{hr}} \times 6 \mathrm{hr}=18 \text { lawns. 3.17.8: Applications of Rational Functions is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts. In a river with unknown current, it takes the boat twice as long to travel 60 miles upstream (against the current) than it takes for the 60 mile return trip (with the current). Ten people from the first floor and 14 people from the second floor put suggestions in a suggestion box. Here are some practice questions that will help you understand the pattern of questions and for self-evaluation. The total time of the trip is 5 hours. our information in it: A boat can travel 16 miles up a river in 2 hours. Carlos can do a certain job in three days, while it takes Alec six days. Find out how you can intelligently organize your Flashcards. The boat travels downstream 150 miles at a net speed of 40 miles per hour. 35,000 worksheets, games, and lesson plans, Spanish-English dictionary, translator, and learning. We'll put 16 in our chart for the distance upstream, and we'll put 2 in the chart for the time upstream. Suppose that he can ca- noe 2 miles upstream in the same amount of time as it takes him to canoe 5 miles downstream. Bill can finish a report in 2 hours. What is the rate of the boat in still water and what is the rate of the current? a. Every applicant should memorize these and should be on fingertips. Boris is kayaking in a river with a 6 mph current. Most questions answered within 4 hours. A speedboat can travel 32 miles per hour in still water. Find the speed of the current. A boat can travel 12 miles upstream in the same amount of time it takes to travel 18 miles downstream. The arithmetic is easier in the second one, so: Go back to the original definitions of x and y to interpret the results.

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