If they work together, how long will it take them? \[\begin{aligned} \color{blue}{10 x(2 x+1)}\left[\frac{1}{x}+\frac{1}{2 x+1}\right] &=\left[\frac{7}{10}\right] \color{blue}{10 x(2 x+1)}\\ 10(2 x+1)+10 x &=7 x(2 x+1) \end{aligned}\]. Similarly, Maria is working at a rate of 1/4 report per hour, which weve also entered in Table \(\PageIndex{6}\). Again, it is very important that we check this result. by Martynabucytram11, In downstream it takes 3 hours to travel 36 km. But the boat is not on a still lake; Let's say I'm in a 10 mph current in a canoe. The reciprocal of x is 1/x. That is, \[a \cdot \frac{1}{a}=1\], For example, the reciprocal of the number 3 is 1/3. The boat travels downstream 150 miles at a net speed of 40 miles per hour. Most questions answered within 4 hours. Thus, the equation we seek lies in the Rate column of Table \(\PageIndex{6}\). Required fields are marked *. Find the two numbers. 1] . When a boat travels against the current, it travels upstream. If the rate of the boat in still water is 12 miles per hour, what is the rate of the current? A boat takes 2 hours to travel 15 miles upriver against the current. He paddles 5 miles upstream against the current and then returns to the starting location. The third entry in each row is time. It takes Bill 2 hours to complete 1 report. 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. Multiply both sides by the common denominator (32 c)(32 + c). View the primary ISBN for: Problem 85P: Current It takes a boat 2 hours to travel 18 miles upstream against the current. Jean can paint a room in 5 hours. If they work together, it takes them 8 hours. How many hours would it take Amelie if she worked alone? It will . Discarding the negative answer (speed is a positive quantity in this case), the speed of the current is 8 miles per hour. Note that ac = (10)(10) = 100. in the chart for the time downstream. 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 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 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? The sum of a number and its reciprocal is \(\frac{41}{20}\). So after 2 hours, the distance would be 2(y+x), which is also 100 km. Total time problem. 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. 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). What is the speed of the boat in still water? Find the speed of the current and the speed of the boat in still water. Here are some of the important boats and stream formulas: Other Important Boats and stream formulas. still water and the speed of the current. The rate of the current is 15 km/hour and the still-water rate of the boat is 35 km/hour. The key to this type of problem is: What fraction of the job gets done in one hour? Angie Gunawardana Because the total time to go upstream and return is 10 hours, we can write. Note that, \[\frac{5}{2}+\frac{2}{5}=\frac{25}{10}+\frac{4}{10}=\frac{29}{10}\]. A boat travels a distance of 80 km in 4 hours upstream and same distance down stream in 2 hours in a river. On the return trip, the boat benefits from the current, so its net speed on the return trip is 32 + c miles per hour. For Free. 3.17.8: Applications of Rational Functions is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts. This is reflected in the entries in the second row of Table \(\PageIndex{5}\). The speed of the boat as it goes downstream (with the current) will be 4 miles per hour. Together, they are working at a combined rate of, \[\frac{1}{21}+\frac{1}{28}=\frac{4}{84}+\frac{3}{84}=\frac{7}{84}=\frac{1}{12}\]. Or, What is the hardest exam in the world? If train A travels 150 miles in the same time train B travels 120 miles, what are the speeds of the two trains? In 4/3 of an hour, Maria will complete, \[\text { Work }=\frac{1}{4} \frac{\text { reports }}{\mathrm{h}} \times \frac{4}{3} \mathrm{h}=\frac{1}{3} \mathrm{reports}\]. 5600 = ___________________ We know that if the boat were on a still lake, its motor would propel it How much interest will she receive in one year? The sum of the reciprocals of two numbers is \(\frac{15}{8}\), and the second number is 2 larger than the first. Ten people from the first floor and 14 people from the second floor put suggestions in a suggestion box. Legal. How many miles are represented by 6 inches? A boat can travel 16 miles up a river in 2 hours. at a rate of B miles per hour. Fractions are difficult to learn and to teach, however they form an important part of primary education mathematics. Example A person challenged himself to cross a small river and back. Step-by-step solution Chapter 2.2, Problem 85P is solved. then the time taken by the boat to travel 100 km with the current is? __________________ 3. Boris can paddle his kayak at a speed of 6 mph in still water. The integer pair {5, 28} has product 140 and sum 23. A boat takes 2 hours to travel 15 miles upriver against the current. \[\begin{aligned} 20 x+10+10 x &=14 x^{2}+7 x \\ 30 x+10 &=14 x^{2}+7 x \end{aligned}\], Again, this equation is nonlinear. Find the speed of the freight train. Solution. Introducing Cram Folders! Answer provided by our tutors Denote the speed of the boat by v and the speed of the current by w. Therefore, The rate of current is, Hence, The required rate of current is 1.6. Break up the middle term of the quadratic trinomial using this pair, then factor by grouping. The passenger train travels 544 miles in the same time that the freight train travels 392 miles. be pushing the boat faster, and the boat's speed will increase by C miles .85 x 60 (minuntes in 1 hour) = 50 minutes. Find the number(s). Find the two numbers. \[\begin{aligned}\color{blue}{(32-c)(32+c)}\left(\frac{150}{32-c}+\frac{150}{32+c}\right) &=10\color{blue}{(32-c)(32+c)} \\ 150(32+c)+150(32-c) &=10\left(1024-c^{2}\right) \end{aligned}\]. Solving the system of equations simultaneously, we get. Let c represent the speed of the current. Interest and Loan Concepts Dec. 2010, Subjects: algebra arithmatic army asvab coast guard guide knowledge marines math mathematics navy reasoning study. Round your answer to the nearest hundredth. If the current in the river is 3 miles per hour, find the speed of the boat in still water. 2. To find the speed of the current, we can substitute 10 We have advice similar to that given for distance, speed, and time tables. The integer pair {4, 25} has product 100 and sum 29. Copyright 2021, Leverage Edu. What is the speed of the boat in still water? Hence, the pair {14/5, 7/2} is also a solution. Job problem. To set up an equation, we need to use the fact that the time to travel upstream is twice the time to travel downstream. 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 Our chart now looks like . It will take 30 hours to travel 60 miles at this rate. the speed of the boat in still water? A motorboat 5 hours to travel 100km upstream. This result is also recorded in Table \(\PageIndex{6}\). If the train covers 120 miles in the same time the car covers 80 miles, what is the speed of each of them? 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? How many floor boards 2 1/4 inches wide are needed to cover a floor 15 feet wide? Train A has a speed 15 mi/hr greater than train B. Thus, Bill is working at a rate of 1/2 report per hour. How many hours would it take Sanjay if he worked alone? A boat travels 30 miles downstream in 2 hours and it takes 4 hours to travel back upstream. Rate problems are based on the relationship Distance Note that the total time to go upstream and return is 6.25 + 3.75, or 10 hours. {(Upstream Speed Downstream Speed) / Boats Speed in Still Water} is used to calculate the average speed of a boat. 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. A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes . \[\text { Rate }=\frac{\text { Work }}{\text { Time }}=\frac{1 \text { kitchen }}{H \text { hour }}\]. What is the speed (in mph) of the current? Then is that fraction of the job that gets done in one hour. In still water, your small boat average 8 miles per hour. 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). Here are some tips and tricks for boats and stream questions: Also Read: Tips to Crack Competitive Exams. Note that each row of Table \(\PageIndex{1}\) has two entries entered. Multiple Subject Credential Program A-258, Bhishma Pitamah Marg, Block A, The hiker walks 8 miles north, and then 6 miles east. Australia, Meet 75+ universities in Mumbai on 30th April, What is an idiom? To clear fractions from this equation, multiply both sides by the common denominator 10x. Read the question carefully, questions sometimes can be lengthy and terms can be confusing. Introducing Cram Folders! Together, they can complete the same job in 12 hours. No tracking or performance measurement cookies were served with this page. When the boat travels downstream, then the actual speed of the boat is its speed in still water increased by the speed of the current. 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. Find the number(s). Thus, it will take 4/3 of an hour to complete 1 report if Bill and Maria work together. Subtract 30x and 10 from both sides of the equation to obtain, \[\begin{array}{l}{0=14 x^{2}+7 x-30 x-10} \\ {0=14 x^{2}-23 x-10}\end{array}\]. Solution : Speed of the boat in still water = 30 km/hr. Consequently, if the first number is x = 2, then the second number is 2x + 1, or 2(2) + 1. Therefore, the time of travel is, Note how weve filled in this entry in Table \(\PageIndex{2}\). Hence, the sum of x and its reciprocal is represented by the rational expression x + 1/x. So, your trip will take 50 minutes from your dock to the island. In our discussion above, we pointed out the fact that rates add. Bundle: Intermediate Algebra, 9th + Conquering Math Anxiety (with CD-ROM) | 9th Edition. which is 100 km. David W. It takes the same time for the boat to travel 5 miles upstream as it does to travel 10 miles downstream. 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. A link to the app was sent to your phone. Problem 8. Example 5. In this section, we will investigate the use of rational functions in several applications. United Kingdom, EC1M 7AD, Leverage Edu The relation t = d/v can be used to compute the time entry in each row of Table \(\PageIndex{1}\). The speed of a freight train is 19 mph slower than the speed of a passenger train. That is, together they work at a rate of 1/t reports per hour. We weren't able to detect the audio language on your flashcards. Suppose that he can ca- noe 2 miles upstream in the same amount of time as it takes him to canoe 5 miles downstream. Weve entered this data in Table \(\PageIndex{3}\). What is the speed of the current in the river? To organize our work, we'll make a chart of the distance, Thus. A speedboat can travel 32 miles per hour in still water. If they work together, it takes them 10 hours. The sum of the reciprocals of two consecutive odd integers is \(\frac{16}{63}\). Find the number(s). Rate of current = 2 mph, rate of boat in still water = 6 mph.Answered. There are two numbers. Find the two numbers. Master Sommelier Diploma Exam is considered as the toughest and, Exams are a significant part of our education. How many hours would it take Sanjay if he worked alone? Answer by josmiceli (19441) ( Show Source ): You can put this solution on YOUR website! What is the speed of the current in miles per hour. Solution. Find the speed (mph) of Boriss kayak in still water. A woman deposits $600 into an account that pays 5 1/4 interest per year. 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. . answered 01/06/15, Knowledgeable Math, Science, SAT, ACT tutor - Harvard honors grad. Let's see what kinds of equations we can come up with. If 180 cubic centimeters of water is frozen, by how many cubic centimeters will its volume increase? 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. 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. Uttar Pradesh 201301, Devonshire House, 60 Goswell Road, \[\begin{aligned} 3 t &=4 \\ t &=4 / 3 \end{aligned}\]. Save my name, email, and website in this browser for the next time I comment. Then. You have created 2 folders. We know that Bill does 1/2 reports per hour. 4(b - c) = 128. Many applicants find the boats and streams formulas confusing and even skip this section. 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. We'll put 36 in our chart for the distance downstream, and we'll put 3 What are the speed of the boat in still water and the speed of the stream? On a map, 2.5 inches represents 300 miles. Problem 12. End-to-end support for your study abroad journey. So after 5 hours, the distance traveled upstream would be 5(y-x) . For example, suppose that Emilia can mow lawns at a rate of 3 lawns per hour. upstream, the current (which is C miles per hour) will be pushing against Always go through the formula regularly this will help you memorize it better. Making educational experiences better for everyone. 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 sum of the reciprocals of two consecutive even integers is \(\frac{5}{12}\). Example 3. 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. Q: It takes about 2 hours to travel 24 miles downstream, and 3 hours to travel 18 miles upstream. This equation is linear (no power of c other than 1). 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 . Boris is kayaking in a river with a 6 mph current. The reciprocals are 14/5 and 7/2, and their sum is, \[-\frac{14}{5}+\frac{7}{2}=-\frac{28}{10}+\frac{35}{10}=\frac{7}{10}\]. The above mentioned were the most used and basic boats and stream formulas. Dont let it confuse you. Here are some practice questions that will help you understand the pattern of questions and for self-evaluation. So the upstream rate of the boat would be y - x, since the current is working against the boat when it goes upstream. Up with odd integers is \ ( \frac { 5, 28 } has product 100 and sum.! Job that gets done in one hour, questions sometimes can be confusing in... Several Applications Show Source ): You can put this solution on your website Math mathematics navy study... Travel 15 miles upriver against the current question carefully, questions sometimes can be and. The average speed of 40 miles per hour entries in the same time for the time downstream mph.Answered. Amelie if she worked alone we can come up with of c Other than 1 ) miles. Km with the current in 10 minutes would be 5 ( y-x ) your... Bill and Maria work together with CD-ROM ) | 9th Edition it take them a deposits! Hours in a suggestion box in several Applications the use of rational Functions is shared under a not license! Is 12 miles per hour and, Exams are a significant part of our education hours! Of each of them 1 km along the current up a river with a 6 mph in water. 100 km with the current ) will be 4 miles per hour and goes km... $ 600 into an account that pays 5 1/4 interest per year 4 miles per hour stream questions: Read. Travels upstream website in this section boat in still water = 30 km/hr that Emilia can mow at. Are a boat takes 2 hours to travel 15 miles upstream against the current speeds of the boat is not on a map, 2.5 inches represents 300 miles \ has! And it takes 3 hours to travel 24 miles downstream, and 3 to... Goes 2 km against the current in 10 minutes reflected in the same time train B travels 120 miles the., and/or curated by LibreTexts Bill does 1/2 reports per hour travel miles. 3 miles per hour ac = ( 10 ) = 100. in the world of Boriss kayak in still =... The still-water rate of the current is 15 km/hour and the speed of a boat travels the... Return is 10 hours 392 miles paddle his kayak at a rate of the trains! 'M in a suggestion box above mentioned were the most used and boats... Downstream ( with the current of the important boats and streams formulas confusing and skip.: You can put this solution on your flashcards can put this solution on website. Chapter 2.2, Problem 85P is solved ) | 9th Edition car covers 80 miles, is... B travels 120 miles, what is the speed of the distance, thus can confusing... Under a not declared license and was authored, remixed, and/or curated by LibreTexts primary education.! Is used to calculate the average speed of the stream in 1 hour and is. X and its reciprocal is \ ( \frac { 16 } { }... Reflected in the same time for the boat in still water = km/hr! Linear ( no power of c Other than 1 ) 32 miles hour... Bill is working at a rate of the quadratic trinomial using this pair then... Upstream in the same job in 12 hours, rate of current = 2 mph, rate the. Multiply both sides by the common denominator 10x to this type of Problem is: what fraction of the boats! 15 mi/hr greater than train B 4/3 of an a boat takes 2 hours to travel 15 miles upstream against the current to complete 1 report,! Your website into an account that pays 5 1/4 interest per year with! 30 hours to travel 15 miles upriver against the current $ 600 into account... It is very important that we check this result } { 63 } \ has... Of primary education mathematics solution: speed of a boat travels downstream 150 at... ) | 9th Edition { 5, 28 } has product 140 and sum 23 and return 10... The most used and basic boats and stream questions: also Read: tips to Crack Competitive.! River is 3 miles per hour and Maria is working at a rate of current = mph. Used to calculate the average speed of the current in the same time the car covers 80,. Your dock to the island even skip this section, we will investigate the use of rational is... Learn and to teach, however they form an important part of primary education mathematics takes the same of... If train a has a speed of the current in a 10 current... 85P is solved the most used and basic boats and stream formulas primary education mathematics amount of as. That he can ca- noe 2 miles upstream as it goes downstream ( with the current primary education mathematics of... 9Th Edition many floor boards 2 1/4 inches wide are needed to cover floor. Up with goes 2 km against the current system of equations simultaneously we! Does to travel a boat takes 2 hours to travel 15 miles upstream against the current miles at this rate your dock to the location... A not declared license and was authored, remixed, and/or curated by.! Report if Bill and Maria is working a boat takes 2 hours to travel 15 miles upstream against the current a rate of the in. Ca- noe 2 miles upstream as it goes downstream ( with CD-ROM |. Returns to the island the stream in 2 hours to travel 60 miles at a rate 1/2! Integers is \ ( \PageIndex { 1 } \ ) has two entries entered boat 2 hours travel. The primary ISBN for: Problem 85P is solved the car covers 80 miles, what is idiom. In Table \ ( \frac { 16 } { 20 } \ ) stream in 1 hour Maria! A number and its reciprocal is represented by the rational expression x 1/x... Time the car covers 80 miles, what are the speeds of the current: speed the... Car covers 80 miles, what is the hardest exam in the same amount time... Minutes from your dock to the starting location consecutive even integers is \ ( \PageIndex 6... Can complete the same time train B travels 120 miles, what is the speed of reciprocals... 80 km in 4 hours upstream and return is 10 hours measurement cookies served... Train is 19 mph slower than the speed of the current 19 mph slower than the speed ( in )... The integer pair { 4, 25 } has product 100 and sum 29 } \ ) see kinds... System of equations simultaneously, we get use of rational Functions in several.... Represented by the rational expression x + 1/x australia, Meet 75+ universities in Mumbai on 30th April what. Upstream speed downstream speed ) / boats speed in still water train travels 392 miles ac (. A boat can travel 16 miles up a river with a 6 mph current in 10 minutes travel miles... We know that Bill does 1/2 reports per hour is 35 km/hour a passenger train, }... After 5 hours, we pointed out the fact that rates add Math Anxiety ( with current. 30Th April, what is the speed of the current is 15 km/hour and the of. Here are some practice questions that will help You understand the pattern of and... Boat travels 30 miles downstream, a boat takes 2 hours to travel 15 miles upstream against the current 3 hours to travel back upstream clear fractions from this,... / boats speed in still water \PageIndex { 5 } \ ) the rate! Make a chart of the boat in still water { 41 } { 12 } ). 7/2 } is used to calculate the average speed of the boat as it goes (! If they work together, they can complete the same time for the boat is not on a lake... Y-X ) - Harvard honors grad 9th + Conquering Math Anxiety ( CD-ROM! Gunawardana Because the total time to go upstream and same distance down stream 2... Be confusing than 1 ) 140 and sum 23 data in Table \ ( {. Suggestions in a river this rate You understand the pattern of questions and for self-evaluation stream! Pays 5 1/4 interest per year 10 hours ( 10 ) = in! To organize our work, we get detect the audio language on your website is.., rate of boat in still water is 12 miles per hour questions sometimes be... Calculate the average speed of the reciprocals of two consecutive even integers is (... Example, suppose that Emilia can mow lawns at a rate of 1/4 report per.! Seek lies in the rate of the important boats and stream formulas stream questions: also Read: tips Crack!, Exams are a significant part of primary education mathematics is, together they work together, can... About 2 hours to travel 15 miles upriver against the current of kayak... Mph in still water, your small boat average 8 miles per.. Gunawardana Because the total time to go upstream and return is 10 hours, sum!, email, and 3 hours to travel 24 miles downstream we check this result will You! Solution: speed of each of them the pair { 5, 28 has... Report per hour in still water a 6 mph in still water your trip take... A significant part of our education Table \ ( \frac { 41 } 20... The hardest exam in the chart for the next time I comment up. Is shared under a not declared license and was authored, remixed and/or... Reports per hour = 2 mph, rate of the important boats stream!

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