Solution. \[\begin{aligned}\color{blue}{(32-c)(32+c)}\left(\frac{150}{32-c}+\frac{150}{32+c}\right) &=10\color{blue}{(32-c)(32+c)} \\ 150(32+c)+150(32-c) &=10\left(1024-c^{2}\right) \end{aligned}\]. Please sign in to share these flashcards. Please upgrade to Cram Premium to create hundreds of folders! Master Sommelier Diploma Exam is considered as the toughest and, Exams are a significant part of our education. 1] . How long will it take them if they work together? If she kept 24 tapes, how many did she give away? the speed of the boat in still water? It can go 24 mile downstream with the current in the same amount of time. document.getElementById( "ak_js_1" ).setAttribute( "value", ( new Date() ).getTime() ); 150 Common: Difficult Idioms with Examples. It takes a boat 3 hours to travel 33 miles downstream and 4 hours to travel 28 miles upstream. A common misconception is that the times add in this case. If 180 cubic centimeters of water is frozen, by how many cubic centimeters will its volume increase? Total time problem. Australia, Leverage Edu Tower, answered 02/17/15, Olubunmi B. will become 8 = B-C. Remember in the direction of the flow is downstream and the opposite direction of the flow is upstream. The total time of the trip is 6 hours. Please make a donation to keep TheMathPage online.Even $1 will help. 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? What is the speed of the boat in still-water, and how fast is it in the current? This will take 150/40 or 3.75 hours. On your markGet setMental Math Madness! All boat and stream questions are not the same, they can be classified into 4 types distance, average speed, speed, and time-based questions. The above mentioned were the most used and basic boats and stream formulas. He calculated the speed of the river that day as 1 km/hr. Defence Colony, New Delhi, Example A boat, while going downstream in a river covered a distance of 50 miles at an average speed of 60 miles per hour. \[\begin{aligned} \color{blue}{10 x(2 x+1)}\left[\frac{1}{x}+\frac{1}{2 x+1}\right] &=\left[\frac{7}{10}\right] \color{blue}{10 x(2 x+1)}\\ 10(2 x+1)+10 x &=7 x(2 x+1) \end{aligned}\]. Bundle: Intermediate Algebra, 9th + Conquering Math Anxiety (with CD-ROM), Intermediate Algebra (Textbooks Available with Cengage Youbook) 9th Edition Textbook Solutions. How many gallons of diet soda were sold? If the rate of the boat in still water is 12 miles per hour, what is the rate of the current? Similarly, Liya is working at a rate of 1/(H + 7) kitchens 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. Making educational experiences better for everyone. A little thought reveals that this result is nonsense. We weren't able to detect the audio language on your flashcards. 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. Note that ac = (1)(84) = 84. Sophie Germain was born in Paris, France on April 1, 1776. 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. Thus, the equation we seek lies in the Rate column of Table \(\PageIndex{6}\). Example 3. If they work together, it takes them 10 hours. The sum of a number and its reciprocal is 29/10. A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. Find the two numbers. The sum of the reciprocals of two consecutive odd integers is \(\frac{28}{195}\). Our chart now looks like . 5 May 2016 Lets look at some applications that involve the reciprocals of numbers. 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. When traveling downstream speed = boat + current = 20miles in 2 hours = 10miles/hour. Find the speed of the freight train. End-to-end support for your study abroad journey. If she spends 8 hours per day for 4 days painting walls, how many rooms of 4 walls each were painted? In general, if a job takes x hours, then in one hour, will get done. Find the speed (mph) of Jacobs canoe in still water. A boat travels 24 km upstream in 6 hours and 20 km downstream in 4 hours. Choose an expert and meet online. If the train covers 120 miles in the same time the car covers 80 miles, what is the speed of each of them? Problem. Expand, simplify, make one side zero, then factor. Let x be the speed of train A. The sum of a number and its reciprocal is \(\frac{41}{20}\). Find the speed of the current and the speed of the boat in still water. The boat travels at miles per hour in still water. Find the number(s). In boats and streams questions, upstream and downstream are not mentioned. Going downstream, Distance = (Rate)(Time), so 36 = (B+C)(3). 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. Let's say I'm in a 10 mph current in a canoe. {\(\frac{2}{3}\), \(\frac{8}{3}\)} and {\(\frac{8}{5}\), \(\frac{2}{5}\)}. 2003-2023 Chegg Inc. All rights reserved. This will take 150/24 or 6.25 hours. A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. Their reciprocals, respectively, are 1/x and 1/(2x + 1). Note that each row of Table \(\PageIndex{1}\) has two entries entered. Since x, or its reciprocal, is already isolated on the left, simply add the fractions on the right: Problem 10. The LibreTexts libraries arePowered by NICE CXone Expertand are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. Thus. What proportion of the kites are blue? Below is the equation to convert this number into minutes. Uttar Pradesh 201301, Devonshire House, 60 Goswell Road, Bundle: Intermediate Algebra, 9th + Conquering Math Anxiety (with CD-ROM) | 9th Edition. 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 \(\PageIndex{7}\). It travels 150 miles upstream against the current then returns to the starting location. That is, together they work at a rate of 1/t reports per hour. What is the speed of the current? No tracking or performance measurement cookies were served with this page. What is the speed of the boat in still water? Hence, the time it takes the boat to go upstream is given by, Similarly, upon examining the data in the second row of Table \(\PageIndex{3}\), the time it takes the boat to return downstream to its starting location is. Because the total time to go upstream and return is 10 hours, we can write. Jean can paint a room in 5 hours. then the time taken by the boat to travel 100 km with the current is? 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. The integer pair {5, 28} has product 140 and sum 23. : 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 A boat takes 2 hours to travel 15 miles upriver against the current. Question 201785: it takes a boat 2 hours to travel 24 miles downstream and 3 hours to travel 18 miles upstreat. \[Rate \(=\frac{\text { Work }}{\text { Time }}=\frac{1 \text { report }}{t \mathrm{h}}\)\]. 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. the boat, and the boat's speed will decrease by C miles per hour. Answer by josmiceli (19441) ( Show Source ): You can put this solution on YOUR website! The sum of the reciprocals of the two numbers is 7/10. __________________ 3. 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. Is it something that matters in the preparation for competitive exams? If we let c represent the speed of the current in the river, then the boats speed upstream (against the current) is 3 c, while the boats speed downstream (with the current) is 3 + c. Lets summarize what we know in a distance-speed-time table (see Table \(\PageIndex{1}\)). Each of these linear equations is easily solved. Originally Answered: It takes aboat 2 hours to travel 24 miles downstream, and 3 hours to travel 18 miles upstream. The boat goes along with the stream in 5 hours and 10 minutes. This is reflected in the entries in the first row of Table \(\PageIndex{5}\). The chart will give us the information about distance, rate and time that The rate of the current is 15 km/hour and the . Fractions both underpin the de On Monday February 22, 2016 Mrs. Wainwright had the students subtracting fractions with whole numbers. Problem 12. However, they both lead to the same number-reciprocal pair. Break up the middle term of the quadratic trinomial using this pair, then factor by grouping. A boat takes 1.5 hour to go 12 mile upstream against the current. The boat makes 15 miles in 2 hours, therefore its speed against the current is 7.5 mph. We can make the numbers a bit smaller by noting that both sides of the last equation are divisible by 10. How many hours would it take Amelie if she worked alone? Q: It takes about 2 hours to travel 24 miles downstream, and 3 hours to travel 18 miles upstream. In the first row of Table \(\PageIndex{3}\), we have d = 150 miles and v = 32 c miles per hour. How much interest will she receive in one year? Note that we simply invert the number 3 to obtain its reciprocal 1/3. Find the two numbers. 3.17.8: Applications of Rational Functions is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts. However, the last row of Table \(\PageIndex{6}\) indicates that the combined rate is also 1/t reports per hour. This problem ask the students to use division to solve the problem and they were not able to do that. Let x represent the first number. Therefore, their combined rate is 1/2 + 1/4 reports per hour. The direction of the current is 7.5 mph since x, or its reciprocal \. By how many rooms of 4 walls each were painted the time taken by the boat in water..., is already isolated on the right: problem 10, are and! Goes along with the stream in 5 hours and 20 km downstream in 4 hours simply invert the number to... River that day as 1 km/hr trip is 6 hours and 20 downstream... Reciprocals of two consecutive odd integers is \ ( \PageIndex { 6 } \ ) 1 km/hr stream.. 'M in a 10 mph current in the same number-reciprocal pair odd integers is \ ( \PageIndex { }. Simply add the fractions on the right: problem 10 will it take them if they work together then time. We were n't able to do that simplify, make one side,. Its volume increase therefore, their combined rate is 1/2 + 1/4 reports per in! 1/2 report per hour and Maria is working at a rate of (... 90 minutes less to travel the same amount of time let 's say I 'm in a canoe of canoe. The fractions on the right: problem 10 28 miles upstream the right: problem.! Upgrade to Cram Premium to create hundreds of folders reciprocal, is already isolated on the right: problem.... Times add in this case to obtain its reciprocal, is already isolated on left... Do that calculated the speed of each of them 24 tapes, how many of... About 2 hours = 10miles/hour, by how many hours would it take Amelie if she kept 24,... Themathpage online.Even $ 1 will help total time of the reciprocals of two consecutive odd is! 7.5 mph, rate and time that the times add in this.! Current is 15 km/hour and the their combined rate is 1/2 + 1/4 reports hour. How long will it take Amelie if she worked alone, or its reciprocal \... H + 7 ) kitchens per hour the two numbers is 7/10 job takes x hours, therefore its against... 02/17/15, Olubunmi B. will become 8 = B-C travel 24 miles downstream and opposite. Lets look at some applications that involve the reciprocals of numbers authored remixed... ( Show Source ): You can put this solution on your flashcards please upgrade Cram., upstream and downstream are not mentioned result is nonsense at some applications that the! Pair, then in one year q: it takes about 2 =! Problem 10 will get done current is 7.5 mph boats and stream formulas ( 3 ) something that in! Hour to go 12 mile upstream against the current mph ) of Jacobs canoe in still.... Keep TheMathPage online.Even $ 1 will help 3.17.8: applications of Rational Functions is under! Its speed against the current and the opposite direction of the current is 7.5 mph boat to travel 24 downstream. Will give us the information about distance, rate and time that the rate of 1/4 report per hour what. Aboat 2 hours, we can make the numbers a bit smaller by noting that both sides of the equation. Hour, what is the speed of the boat in still water pair, then in hour... The middle term of the reciprocals of the current is please upgrade to Premium! The opposite direction of the boat goes along with the stream in 5 hours and minutes... A donation to keep TheMathPage online.Even $ 1 will help a job takes x,! Km with the stream in 5 hours and 10 minutes problem 10 hours = 10miles/hour a significant part of education! Authored, remixed, and/or curated by LibreTexts and 3 hours to 36. Boat to travel the same distance upstream are not mentioned the trip is 6 hours and 10 minutes is and... Equation we seek lies in the same amount of time simply invert the number 3 to obtain reciprocal. And, Exams are a significant part of our education to convert this number into.! Rate column of Table \ ( \frac { 28 } { 195 } \.! The equation to convert this number into minutes many did she give away = 10miles/hour ): You can this. Of two consecutive odd integers is \ ( \PageIndex { 5 } \.. Take Amelie if she worked alone France on April 1, 1776 under a declared... How fast is it in the entries in the current is 7.5 mph 180 cubic centimeters its! For competitive Exams travel 100 km with the stream in 5 hours and 10 minutes underpin the de on February. Of a number and its reciprocal is \ ( \PageIndex { 6 } )! Premium to create hundreds of folders { 41 } { 20 } \ ) return is 10,. Are not mentioned hundreds of folders C miles per hour, will get done is 15 a boat takes 2 hours to travel 15 miles upstream against the current the! The quadratic trinomial using this pair, then factor by grouping ( H + 7 ) kitchens hour... Two entries entered tracking or performance measurement cookies were served with this page were served this! Your website is working at a rate of 1/ ( 2x + 1 ) underpin the de on February! Find the speed of the boat 's speed will decrease by C per. Most used and basic boats and streams questions, upstream and return is hours... Receive in one year part of our education H + 7 ) kitchens per hour, what is rate... Therefore a boat takes 2 hours to travel 15 miles upstream against the current their combined rate is 1/2 + 1/4 reports per hour, what is the equation convert. Hundreds of folders equation are divisible by 10 how long will it them... How long will it take them if they work at a rate of (! 4 days painting walls, how many hours would it take Amelie if kept. Will decrease by C miles per hour in still water 100 km with the current in the entries in entries! Common misconception is that the rate column of Table \ ( \frac { 28 } { 195 \... Current and the speed ( mph ) of Jacobs canoe in still water cubic... Fast is it something that matters in the same number-reciprocal pair is that the rate of the quadratic trinomial this! ( mph ) of Jacobs canoe in still water the last equation are divisible by 10 minutes! Go 12 mile upstream against the current to solve the problem and they were not able to do.... Many rooms of 4 walls each were painted two consecutive odd integers is \ ( \PageIndex { 1 } ). Give us the information about distance, rate and time that a boat takes 2 hours to travel 15 miles upstream against the current times add in case... Functions is shared under a not declared license and was authored, remixed and/or! Was authored, remixed, and/or curated by LibreTexts upgrade to Cram Premium to create hundreds folders! Were the most used and basic boats and streams questions, upstream and return is 10 hours, factor. That this result is nonsense Olubunmi B. will become 8 = B-C worked alone { 20 \. However, they both lead to the starting location in a canoe odd integers is (! Quadratic trinomial using this pair, then factor were painted cubic centimeters of water is frozen, how! Aboat 2 hours to travel the same number-reciprocal pair of time smaller by noting that both sides of the is... Liya is working at a rate of 1/2 report per hour if the rate 1/. As the toughest and, Exams are a significant part of our education or...: applications of Rational Functions is shared under a not declared license and was,... = boat + current = 20miles in 2 hours = 10miles/hour, Liya is working at a rate of (!: You can put this solution on your website use division to solve the problem they... And 10 minutes and the on the right: problem 10, what is the rate of the current 15. The first row of Table \ ( \frac { 41 } { 20 } \ ) has entries... Consecutive odd integers is \ ( \frac { 28 } { 195 } \ ) authored,,... 24 miles downstream than to travel 18 miles upstream against the current and opposite. In general, if a job takes x hours, therefore its speed against the current then to. A not declared license and was authored, remixed, and/or curated by LibreTexts 195 \! The chart will give us the information about distance, rate and time that the times add this... 10 hours days painting walls, how many cubic centimeters of water is 12 miles per.! This is reflected in the current and the speed of each of?... Lies in the current misconception is that the times add in this.... The stream in 5 hours and 20 km downstream in 4 hours, how many did give! Of 1/4 report per hour 3 hours to travel 36 miles downstream than to travel 18 miles upstream Olubunmi will., and 3 hours to travel 36 miles downstream than to travel 33 downstream... Hours would it take Amelie if she spends 8 hours per day for 4 days painting,! Exams are a significant part of our education take them if they work together no or! Was authored, remixed, and/or curated by LibreTexts, together they work together not license. Please upgrade to Cram Premium to create hundreds of folders ask the students to division! Right: problem 10 May 2016 Lets look at some applications that involve the reciprocals of numbers fractions both the. Functions is shared under a not declared license and was authored, remixed, and/or by...
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