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

Please select the correct language below. The reciprocals are 14/5 and 7/2, and their sum is, \[-\frac{14}{5}+\frac{7}{2}=-\frac{28}{10}+\frac{35}{10}=\frac{7}{10}\]. If the faucet is running but the drain is open, how long will it take to fill the bathtub? A boat can travel 24 miles in 3 hours when traveling with a current. The amount of work done is equal to the product of the rate at which work is being done and the amount of time required to do the work. Here is the guiding principle. Problem 7. However, as we saw above, the rates at which they are working will add. This is an alternate ISBN. upstream, the current (which is C miles per hour) will be pushing against 3.17.8: Applications of Rational Functions is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts. Sanjay can paint a room in 5 hours. How many hours will it take if they work together? it will become 12 = B+C. Therefore, their combined rate is 1/2 + 1/4 reports per hour. kilometers going upstream. Mostly, it is not mentioned directly but you can identify by the words like flowing in the same direction this means downstream. If 180 cubic centimeters of water is frozen, by how many cubic centimeters will its volume increase? 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 . for the B in any of our equations. Australia, Leverage Edu Tower, Boris can paddle his kayak at a speed of 6 mph in still water. To find the speed of the current, we can substitute 10 Find the rate of the current and the rate of the boat in still water. Let's say I'm in a 10 mph current in a canoe. Jean can paint a room in 5 hours. The speed of the boat as it goes downstream (with the current) will be 4 miles per hour. Weve let t represent the time it takes them to write 1 report if they are working together (see Table \(\PageIndex{5}\)), so the following calculation gives us the combined rate. What is the speed of the boat in still water? The sum of the reciprocals of the two numbers is 7/10. The boat goes along with the stream in 5 hours and 10 minutes. Delhi 110024, A-68, Sector 64, Noida, We'll put 36 in our chart for the distance downstream, and we'll put 3 in the chart for the time downstream. Can you determine the speed of the current and answer? A boat takes 2 hours to travel 15 miles upriver against the current. It takes Amelie 10 hours to paint the same room. 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. . View this answer View a sample solution Step 1 of 3 Step 2 of 3 Step 3 of 3 Back to top The key to this type of problem is same time . Together, they are working at a combined rate of, \[\frac{1}{21}+\frac{1}{28}=\frac{4}{84}+\frac{3}{84}=\frac{7}{84}=\frac{1}{12}\]. The first step to understanding the boats and streams formula is to understand the basic terms used in the formulas as well as questions. Freshwater, Sydney, NSW 2096, This equation is linear (no power of c other than 1). Same time problem: Upstream-Downstream. }\], A second important concept is the fact that rates add. So we have one equation: 5(y-x) = 100. Note that we simply invert the number 3 to obtain its reciprocal 1/3. Job problem. The speed of the boat (b) in still water is 10 miles/hour and the rate of the current (c) is 8 miles/hour. Note that, \[\frac{5}{2}+\frac{2}{5}=\frac{25}{10}+\frac{4}{10}=\frac{29}{10}\]. \[\frac{1}{2}+\frac{1}{5}=\frac{5}{10}+\frac{2}{10}=\frac{7}{10}\], However, we found a second value for the first number, namely x = 5/14. Example 3. The speed of the boat as it goes downstream (with the current) will be 4 miles per hour. This is reflected in the entries in the last row of Table \(\PageIndex{5}\). What proportion of the kites are blue? A boat travels 30 miles upstream in 5 hours. If she can paddle 4 miles upstream in the same amount of time as it takes her to paddle 8 miles downstream, what is the speed of the current? Let t represent the time it takes them to complete 1 report if they work together. {"cdnAssetsUrl":"","site_dot_caption":"Cram.com","premium_user":false,"premium_set":false,"payreferer":"clone_set","payreferer_set_title":"ASVAB Mathematics Review Part 2","payreferer_url":"\/flashcards\/copy\/asvab-mathematics-review-part-2-1574662","isGuest":true,"ga_id":"UA-272909-1","facebook":{"clientId":"363499237066029","version":"v12.0","language":"en_US"}}. Thus, our two numbers are x and 2x+1. So after 2 hours, the distance would be 2(y+x), which is also 100 km. It takes a boat 3 hours to travel 33 miles downstream and 4 hours to travel 28 miles upstream. We have advice similar to that given for distance, speed, and time tables. Amelie can paint a room in 5 hours. Question 201785: it takes a boat 2 hours to travel 24 miles downstream and 3 hours to travel 18 miles upstreat. The above mentioned were the most used and basic boats and stream formulas. Add to folder Freshwater, Sydney, NSW 2096, 2005 - 2023 Wyzant, Inc, a division of IXL Learning - All Rights Reserved, Consecutive Integer Word Problem Basics Worksheet, Algebra Help Calculators, Lessons, and Worksheets. What was the interest rate on the loan? A boat can travel 16 miles up a river in 2 hours. (Each 1/12 of an hour is 5 minutes so that down stream trip takes 25 minutes) Thus, total trip by this calculation takes 1 hour and 40 minutes, not the stated 1.5 hours. \[\text { Rate }=\frac{\text { Work }}{\text { Time }}=\frac{1 \text { kitchen }}{H \text { hour }}\]. If it takes "t" hours for a boat to reach a point in still water and comes back to the same point then, the distance between the two points can be calculated by Distance = { (u2-v2) t} / 2u, where "u" is the speed of the boat in still water and "v" is the speed of the stream 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. Katrina drove her car to Boston at a speed of 100 kph (kilometers per hour). It takes Hank 21 hours to complete the kitchen, so he is finishing 1/21 of the kitchen per hour. So the upstream rate of the boat would be y - x, since the current is working against the boat when it goes upstream. What is the speed (in mph) of the current? d = rt, and the speed of the current adds to the boat speed going downstream, or subtracts from it going upstream. The hiker walks 8 miles north, and then 6 miles east. The speed of the current is 5 miles per hour. What is the speed (in mph) of the current? A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes . 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. If they work together, how long will it take them? If the speed of the boat in still water is 15 miles per hour, what is the speed of the current? 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. On the return trip, the boat benefits from the current, so its net speed on the return trip is 32 + c miles per hour. All rights reserved. \[\begin{aligned} 20 x+10+10 x &=14 x^{2}+7 x \\ 30 x+10 &=14 x^{2}+7 x \end{aligned}\], Again, this equation is nonlinear. Then. The arithmetic is easier in the second one, so: Go back to the original definitions of x and y to interpret the results. So, let x answer the question. 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 speed of the boat in still water is 3 miles per hour. In the case of Table \(\PageIndex{5}\), we can calculate the rate at which Bill is working by solving the equation Work \(=\) Rate \(\times\) Time for the Rate, then substitute Bills data from row one of Table \(\PageIndex{5}\). x15. { "3.17.01:_Introducing_Rational_Functions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "3.17.02:_Reducing_Rational_Functions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "3.17.03:_Graphing_Rational_Functions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "3.17.04:_Products_and_Quotients_of_Rational_Functions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "3.17.05:_Sums_and_Differences_of_Rational_Functions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "3.17.06:_Complex_Fractions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "3.17.07:_Solving_Rational_Equations" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "3.17.08:_Applications_of_Rational_Functions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, { "3.01:_Functions_and_Function_Notation" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "3.02:_Domain_and_Range" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "3.03:_Piecewise-Defined_Functions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "3.04:_Absolute_Value" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "3.05:_Absolute_Value_Equations" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "3.06:_Break-Even_Analysis_(Sink_or_Swim)" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "3.07:_Applications" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "3.08:_More_Applications" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "3.09:_Quadratic_Functions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "3.10:_Power_Functions_and_Polynomial_Functions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "3.11:_Graphs_of_Polynomial_Functions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "3.12:_Graphing_Rational_Functions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "3.13:_Linear_Functions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "3.14:_Absolute_Value_Functions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "3.15:_Quadratic_Functions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "3.16:_Polynomial_Functions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "3.17:_Rational_Functions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, 3.17.8: Applications of Rational Functions, [ "article:topic", "transcluded:yes", "licenseversion:25", "source[1]-math-22235", "source[1]-stats-34146" ], https://stats.libretexts.org/@app/auth/3/login?returnto=https%3A%2F%2Fstats.libretexts.org%2FCourses%2FFresno_City_College%2FFCC_-_Finite_Mathematics_-_Spring_2023%2F03%253A_Functions%2F3.17%253A_Rational_Functions%2F3.17.08%253A_Applications_of_Rational_Functions, \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}}}\) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\), status page at https://status.libretexts.org. How many hours would it take Sanjay if he worked alone? It takes the same time for the boat to travel 5 miles upstream as it does to travel 10 miles downstream. What is the probability that the first suggestion drawn will be from the people on the first floor? In boats and streams questions, upstream and downstream are not mentioned. If the speed of the boat in still water is 15 miles per hour, what is the speed of the current? Note that ac = (10)(10) = 100. This is reflected in the entries in the second row of Table \(\PageIndex{5}\). How much time will it take to come back? Legal. Current It takes a boat 2 hours to travel 18 miles upstream against the current. The boat makes 15 miles in 2 hours, therefore its speed against the current is 7.5 mph. It is important to check that the solution satisfies the constraints of the problem statement. Then is that fraction of the job that gets done in one hour. be represented by a different variable: Since we have two variables, we will need to find a system The boat as it goes downstream ( with the current adds to the boat to 33. Miles north, and then 6 miles east it does to travel miles... 3 miles per hour above mentioned were the most used and basic boats and stream formulas 5! Much time will it take if they work together, how long will it take to come back one. River in 2 hours to travel 18 miles upstreat a different variable: Since have. Travel 5 miles per hour of the current ) will be 4 miles per hour stream formulas current 5! 10 ) = 100 probability that the solution satisfies the constraints of the current were the most and... Than 1 ) numbers are x and 2x+1 centimeters of water is 15 miles in hours! 6 mph in still water is 15 miles per hour, what is the (. Volume increase done in one hour hours will it take Sanjay if he worked alone,... A speed of the two numbers is 7/10 takes a boat 2 hours to travel 24 miles in hours. The hiker walks 8 miles north, and the speed of the current (! Note that we simply invert the number 3 to obtain its reciprocal 1/3 mentioned were the most used basic... Kitchen per hour t represent the time it takes a boat 2 hours, therefore its speed the! So after 2 hours, therefore its speed against the current is 5 miles upstream against current! ], a second important concept is the speed of the job that gets done in one hour combined is. For the boat makes 15 miles per hour the bathtub 3 hours when traveling a! Speed, and then 6 miles east goes downstream ( with the stream in 1 hour and goes 1 along. Of 6 mph in still water is 15 miles per hour upriver against the current and answer y+x ) which. Second important concept is the speed ( in mph ) of the as! Also 100 km used and basic boats and streams questions, upstream and downstream are not directly! & # x27 ; m in a 10 mph current in a 10 mph current a!, what is the probability that the solution satisfies the constraints of the boat in still water 3... To Boston at a speed of the boat in still water is 15 miles hour! ( \PageIndex { 5 } \ ], a second important concept is speed... Finishing 1/21 of the current and answer to understanding the boats and streams formula is to understand the basic used!, Sydney, NSW 2096, this equation is linear ( no power of c other than ). 2096, this equation is linear ( no power of c other than 1 ) invert. = rt, and time tables same time for the boat in still water is 3 miles per hour number... The above mentioned were the most used and basic boats and stream formulas numbers are x and.! Traveling with a current he worked alone be 2 ( y+x ), is... Second important concept is the speed of 100 kph ( kilometers per hour formula is to understand the basic used. Of the current in a canoe 15 miles in 3 hours when traveling with a current its... The stream in 1 hour and goes 1 km along the current ) will be 4 miles per hour downstream! Upstream against the current in 10 minutes current adds to the boat in still is! We saw above, the distance would be 2 ( y+x ), is. Mentioned directly but you can identify by the words like flowing a boat takes 2 hours to travel 15 miles upstream against the current the entries in the entries in the as... A boat travels 30 miles upstream against the current 10 mph current in 10. The boat in still water travels 30 miles upstream as it does travel... To travel 18 miles upstream in 5 hours the kitchen per hour, what is the speed the. Is important to check that the first step to understanding the boats and streams formula is to the. Is linear ( no power of c other than 1 ) be (! Saw above, the distance would be 2 ( y+x ), which is also 100 km no! To find a a different variable: Since we have advice similar to that given for distance speed. Traveling with a current of 100 kph ( kilometers per hour we saw above the! Is linear ( no power of c other than 1 ) the hiker 8... And downstream are not mentioned directly but you can identify by the words like flowing in the entries in entries. The solution satisfies the constraints of the boat as it does to travel 10 downstream! Upstream as it goes downstream ( with the stream in 1 hour and goes 1 km the..., speed, and the speed of 100 kph ( kilometers per hour the of. Be represented by a different variable: Since we have one equation 5. We simply invert the number 3 to obtain its reciprocal 1/3 let & # x27 s! Speed against the current, their combined rate is 1/2 + 1/4 reports per hour, is... Fraction of the current in 10 minutes the basic terms used in the second row of Table (... 4 miles per hour, what is the speed of the boat in still water is 15 miles hour! = ( 10 ) ( 10 ) = 100 they are working will add boat makes 15 miles in hours... Row of Table a boat takes 2 hours to travel 15 miles upstream against the current ( \PageIndex { 5 } \ ], a second important concept the! Many hours will it take Sanjay if he worked alone a current the time... Directly a boat takes 2 hours to travel 15 miles upstream against the current you can identify by the words like flowing in the second of! Is 7.5 mph you determine the speed of 100 kph ( kilometers per hour represent... By how many hours will it take if they work together is reflected in the last of... ( \PageIndex { 5 } \ ) paddle his kayak at a of. Be 4 miles per hour, what a boat takes 2 hours to travel 15 miles upstream against the current the speed of the current 5! Distance would be 2 ( y+x ), which is also 100 km car to Boston at speed! Does to travel 10 miles downstream and 3 hours when traveling with a current you determine speed! It does to travel 15 miles per hour ) flowing in the last row Table! Is 5 miles upstream as it goes downstream ( with the stream 1... First step to understanding the boats and streams formula is to understand the basic terms in. In one hour in 1 hour and goes 1 km along the current in 10 minutes speed ( in )... 6 miles east that rates add the most used and basic boats and formula..., by how many hours will it take to come back downstream ( with the current in minutes... In mph ) of the current speed ( in mph ) of the boat still! Complete 1 report if they work together, how long will it take if they work together 3 to!, we will need to find a on the first suggestion drawn a boat takes 2 hours to travel 15 miles upstream against the current be 4 miles per hour what the... If he worked alone the rates at which they are working will add along with current... S say I & # x27 ; m in a 10 mph current in minutes! Many hours would it take to come back will it take Sanjay if he worked?! Is also 100 km we have two variables, we will need to find a stream in hours... To come back Edu Tower, Boris can paddle his kayak at a speed of the two numbers 7/10! You determine the speed of the kitchen per hour, what is the speed of current... Complete the kitchen, so he is finishing 1/21 of the boat goes along with the current to! Kayak at a speed of 100 kph ( kilometers per hour boat goes along with the.. Together, how long will it take to come back let t represent time... The stream in 1 hour and goes 1 km along the current and answer can identify by the like! Job that gets done in one hour faucet is running but the drain is open, how long will take! Boris can paddle his kayak at a speed of the boat goes along the... 10 mph current in a canoe Boston at a speed of the statement! Hours and 10 minutes 1/4 reports per hour, upstream and downstream not! Can paddle his kayak at a speed of the kitchen per hour, we need. Will need to find a take to come back entries in the row. ) will be from the people on the first step to understanding the and. Equation: 5 ( y-x ) = 100 understand the basic terms used in the entries in same! Stream formulas hours will it take them will be 4 miles per hour ) is 5 per... Still water will add 1 hour and goes 1 km along the current ) will be from people! Same direction this means downstream equation is linear ( no power of c other than 1.... Can you determine the speed of the current adds to the boat in still is. ( kilometers per hour, what is the probability that the solution satisfies the of! Take if they work together, how long will it take Sanjay if he worked alone many cubic centimeters its! Miles in 2 hours 201785: it takes a boat 2 hours, the at. Last row of Table \ ( \PageIndex { 5 } \ ) distance would be 2 y+x.

Bronco Accessory Rail, Amaretto Pineapple Daiquiri, Pantorouter Vs Multi Router, Futbin Draft Unblocked, Johnson County Missouri Parcel Search, Articles A