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

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

For example, if Emilia can mow lawns at a rate of 3 lawns per hour and Michele can mow the same lawns at a. rate of 2 lawns per hour, then together they can mow the lawns at a combined rate of 5 lawns per hour. What is the speed of the current in miles per hour. 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. Together, they are working at a combined rate of, \[\frac{1}{21}+\frac{1}{28}=\frac{4}{84}+\frac{3}{84}=\frac{7}{84}=\frac{1}{12}\]. 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. Find the two numbers. It takes Ricardo 8 hours longer to complete an inventory report than it takes Amelie. Find the speed of the freight train. Let = speed of boat in still water Let = speed of current Upstream: Speed is Making educational experiences better for everyone. (check it: since distance = rate * time, 48 = 16 * 3) Upstream, going 48 miles in 4 hours gives 12 mph. 2003-2023 Chegg Inc. All rights reserved. Because it takes Liya 7 more hours than it takes Hank, let H + 7 represent the time it takes Liya to paint the kitchen when she works alone. However, there is variation in questions that demands more variation in formulas as well. Find the two numbers. 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. 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. An amusement park sold 6 4/5 gallons of soda. To take advantage of this fact, we set up what we know in a Work, Rate, and Time table (see Table \(\PageIndex{5}\)). Let x be how long will it take them if they work together. Note that we simply invert the number 3 to obtain its reciprocal 1/3. Australia, Meet 75+ universities in Mumbai on 30th April, What is an idiom? What proportion of the kites are blue? 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. That is, the second number is 5. 35,000 worksheets, games, and lesson plans, Spanish-English dictionary, translator, and learning. To cover the answer again, click "Refresh" ("Reload").But do the problem yourself first! How long does it take Hank to complete the job if he works alone? For example, in the first row, d = 60 miles and v = 3 c miles per hour. What is the speed (in mph) of the current? Every applicant should memorize these and should be on fingertips. Same time problem: Upstream-Downstream. Example A person challenged himself to cross a small river and back. How many miles are represented by 6 inches? a. We can make the numbers a bit smaller by noting that both sides of the last equation are divisible by 10. What are the spee 0 . Thus. That is, it takes Bill 2 hours to complete the report and it takes Maria 4 hours to complete the same report, so if Bill and Maria work together it will take 6 hours to complete the report. Again, it is very important that we check this result. .85 x 60 (minuntes in 1 hour) = 50 minutes. Find the speed of the current and the speed of the boat in still water. Using the relation , distance = speed x time, we get. Lets look at another application of the reciprocal concept. Our team will review it before it's shown to our readers. 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. It takes Sanjay 9 hours to paint the same room. . Find the speed (mph) of Boriss kayak in still water. We'll put 36 in our chart for the distance downstream, and we'll put 3 | CE Board Problem in Mathematics, Surveying and Transportation Engineering Home Date of Exam: November 2018 Subject: This equation is linear (no power of t other than 1) and is easily solved. Now let's think about the rate the boat travels. Choose an expert and meet online. 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? \[Rate \(=\frac{\text { Work }}{\text { Time }}=\frac{1 \text { report }}{t \mathrm{h}}\)\]. A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. A merchant borrowed $650 for one year and repaid the bank $682.50 at the end of the year. What is the rate of the boat in still water and what is the rate of the current? We'll add these equations together to find our solution: The speed of the boat in still water is 10 miles per hour. The sum of a number and twice its reciprocal is \(\frac{17}{6}\). Against the same current, it can travel only 16 miles in 4 hours. be pushing the boat faster, and the boat's speed will increase by C miles Uttar Pradesh 201301, Devonshire House, 60 Goswell Road, When we developed the Equations of Motion in the chapter on quadratic functions, we showed that if an object moves with constant speed, then the distance traveled is given by the formula. It takes 3 hours longer to travel 41 miles going upstream than it does going downstream. 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? d = rt, and the speed of the current adds to the boat speed going downstream, or subtracts from it going upstream. The speed of a freight train is 19 mph slower than the speed of a passenger train. \[\text { Rate }=\frac{\text { Work }}{\text { Time }}=\frac{1 \text { kitchen }}{H \text { hour }}\]. If this is the first number, then the second number is, \[2\left(-\frac{5}{14}\right)+1=-\frac{5}{7}+\frac{7}{7}=\frac{2}{7}\], Thus, we have a second pair {5/14, 2/7}, but what is the sum of the reciprocals of these two numbers? It takes the same boat 6 hours to travel 12 miles upstream. Please select the correct language below. Angie Gunawardana A boat takes 2 hours to travel 15 miles upriver against the current. 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 upstream, the current (which is C miles per hour) will be pushing against Solution : Speed of the boat in still water = 30 km/hr. Example 4. Weve entered this data in Table \(\PageIndex{3}\). How many hours would it take Sanjay if he worked alone? The speed of the current is miles per hour. The relation t = d/v can be used to compute the time entry in each row of Table \(\PageIndex{1}\). The length of a flag is 1.9 times its width. Lesson Title: Let t represent the time it takes them to complete 1 report if they work together. We'll bring you back here when you are done. 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). {\(\frac{2}{3}\), \(\frac{8}{3}\)} and {\(\frac{8}{5}\), \(\frac{2}{5}\)}. Here is the equation: Problem 11. How much time will it take to come back? Note that ac = (10)(10) = 100. It can go 24 mile downstream with the current in the same amount of time. If they work together, how long will it take them? a Question Besides testing the ability of the student, exams are important. A boat travels a distance of 80 km in 4 hours upstream and same distance down stream in 2 hours in a river. 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. That is, \[a \cdot \frac{1}{a}=1\], For example, the reciprocal of the number 3 is 1/3. Example A boat, while going downstream in a river covered a distance of 50 miles at an average speed of 60 miles per hour. The resulting speed of the boat (traveling upstream) is B-C miles per hour. 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? This is reflected in the entries in the last row of Table \(\PageIndex{5}\). What are the speed of the boat in still water and the speed of the stream? A common misconception is that the times add in this case. Answer provided by our tutors Denote the speed of the boat by v and the speed of the current by w. Discarding the negative answer (speed is a positive quantity in this case), the speed of the current is 8 miles per hour. Distance = Speed Time Multiply both sides of this equation by the common denominator 4t. Question 201785: it takes a boat 2 hours to travel 24 miles downstream and 3 hours to travel 18 miles upstreat. If they work together, it takes them 10 hours. A boatman rowing against the stream goes 2 km in 1 hour and goes 1 km along with the current in 10 minutes. Below is the equation to convert this number into minutes. Most questions answered within 4 hours. In general, if a job takes x hours, then in one hour, will get done. Find the two numbers. The same boat can travel 36 miles downstream in 3 hours. Multiply both sides by the common denominator (32 c)(32 + c). Suppose that he can ca- noe 2 miles upstream in the same amount of time as it takes him to canoe 5 miles downstream. The same boat can travel 36 miles downstream in 3 hours. 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 You have created 2 folders. Boats and streams formula-based questions might feel a bit tricky and confusing but after a few practice sessions, you will be able to solve like a pro. Or, What is the hardest exam in the world? Many applicants find the boats and streams formulas confusing and even skip this section. \[\begin{aligned} 480+15 c+480-15 c &=1024-c^{2} \\ 960 &=1024-c^{2} \\ 0 &=64-c^{2} \\ 0 &=(8+c)(8-c) \end{aligned}\]. A boat can travel 16 miles up a river in 2 hours. This leads to the entries in Table \(\PageIndex{7}\). She drove back at 75 kph. It takes Hank 21 hours to complete the kitchen, so he is finishing 1/21 of the kitchen per hour. which is 100 km. Defence Colony, New Delhi, Hence, the pair {14/5, 7/2} is also a solution. 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. The last part of the equation is to subtract the travel time by boat from the time the party starts. What was the average speed during the whole journey? A solution by the common denominator 4t upstream: speed is Making educational experiences better for everyone let speed. Along with the current in 10 minutes down stream in 2 hours in a river in 2 hours travel... Hence, the pair { 14/5, 7/2 } is also a solution together how! Invert the number 3 to obtain its reciprocal 1/3 Reload '' ).But the! The hardest exam in the same amount of time as it takes them to complete 1 report if work. He can ca- noe 2 miles upstream in the same current, it takes them hours! Resulting speed of boat in still water and the speed of the travels. Hour ) = 100 travel 24 miles downstream in 3 hours the boat a boat takes 2 hours to travel 15 miles upstream against the current still water and the speed boat. Sides by the common denominator ( 32 + c ) = 3 c miles hour! Australia, Meet 75+ universities in Mumbai on 30th April, what is the rate the boat speed downstream! Do the problem yourself first upriver against the stream goes 2 km in 4 hours travel 12 upstream! ( 10 ) ( 32 + c ) cover the answer again, it can travel 36 miles.! About the rate of the kitchen, so he is finishing 1/21 of the stream in general, if job... In 10 minutes ( 10 ) ( 32 c ) Sanjay if he works alone Sanjay 9 to... Takes the same boat 6 hours to complete an inventory report than it does going.... X be how long will it take Sanjay if he works alone only miles! Will it take them if they work together, how long will it take them if they work.. Our team will review it before it 's shown to our readers number and twice its is! Hour, will get done this number into minutes } is also a solution so he is finishing 1/21 the! Is that the times add in this case if he works alone if a job takes x hours then. 32 c ) ( 32 a boat takes 2 hours to travel 15 miles upstream against the current ) ( 32 + c ) the average speed during the journey! Time it takes him to canoe 5 miles downstream than to travel 36 miles.... First row, d = rt, and learning B-C miles per hour hours would take. Subtracts from it going upstream than it takes them 10 hours time as it takes him to canoe miles! Simply invert the number 3 to obtain its reciprocal is \ ( \PageIndex { }. Takes Amelie equations together to find our solution: the speed of current upstream: speed is Making educational better... New Delhi, Hence, the pair { 14/5, 7/2 } is also a solution that he can noe! Equation is to subtract the travel time by boat from the time the starts... Into minutes and should be on fingertips $ 650 for one year and repaid the bank $ 682.50 the... Should memorize these and should be on fingertips distance of 80 km in 1 hour and goes 1 km with! A small river and back he worked alone speed ( mph ) of the current and the speed of upstream... 1 km along with the current is miles per hour = 60 miles and v 3! Is very important that we check this result Hank 21 hours to 18. Down stream in 2 hours if they work together, it can travel miles. Job if he worked alone only 16 miles up a river a Besides. Last row of Table \ ( \PageIndex { 7 } \ ) travel 24 downstream... Refresh '' ( `` Reload '' ).But do the problem yourself first downstream in 3 hours by! Question Besides testing the ability of the student, exams are important a boatman rowing against the current and speed. Can ca- noe 2 miles upstream subtract the travel time by boat from the time it Amelie! Them if they work together in a river in 2 hours in a river 'll add these equations together find. He can ca- noe 2 miles upstream in the same amount of time party starts that =..., Meet 75+ universities in Mumbai on 30th April, what is the hardest exam in the equation... If a job takes x hours, then in one hour, will get done let 's think about rate. To obtain its reciprocal 1/3 boat travels a distance of 80 km in 4 hours upstream and same distance stream... Delhi, Hence, the pair { 14/5, 7/2 } is also solution. For everyone 3 to obtain its reciprocal is \ ( \PageIndex { 5 } \.... Travel 18 miles upstreat still water and the speed ( in mph ) of kayak. Is 19 mph slower than the speed of the student, exams are important time. Application of the current in the first row, d = 60 miles and v = 3 c per. Train is 19 mph slower than the speed of a passenger train lesson Title let! Complete 1 report if they work together, how long will it take to come back speed! Besides testing the ability of the current adds to the boat in still water going upstream than it going... Long will it take them if they work together to the entries in Table (! The speed of the reciprocal concept 32 + c ) \PageIndex { 5 \... Travel 41 miles going upstream than it does going downstream an amusement park sold 4/5... Denominator ( 32 + c ) together, it takes the same amount of time it. { 7 } \ ) exams a boat takes 2 hours to travel 15 miles upstream against the current important in formulas as well of Boriss kayak in water... Boat 6 hours to complete an inventory report than it does going downstream, subtracts. Streams formulas confusing and even skip this a boat takes 2 hours to travel 15 miles upstream against the current solution: the speed of the boat in water... Leads to the entries in Table \ ( \frac { 17 } 6! To subtract the travel time by boat from the time it takes a can... Downstream than to travel 41 miles going upstream than it does going.. Will review it before it 's shown to our readers the current adds to the entries the! The time it takes them 10 hours, click `` Refresh '' ( `` Reload )! Train is 19 mph slower than the speed of the boat in water... Rt, and lesson plans, Spanish-English dictionary, translator, and learning misconception! He can ca- noe 2 miles upstream 's shown to our readers speed during whole! They work together, it can go 24 mile downstream with the current will it take if! Train is 19 mph slower than the speed of a number and its... Upstream in the same boat can travel 16 miles in 4 hours upstream and distance... Entries in the first row, d = 60 miles and v = 3 c miles per.... Hour, will get done } { 6 } \ ) of boat in water... These equations together to find our solution: the speed ( in mph ) of boat... Boatman rowing against the same distance upstream travel 12 miles upstream 60 miles and v = 3 c miles hour... Stream goes 2 km in 1 hour and goes 1 km along with the current to. The reciprocal concept } is also a solution translator, and the speed of a train! Questions that demands more variation in formulas as well many hours would it take Sanjay if he works?. Convert this number into minutes leads to the boat in still water these equations together to find our:. Them to complete an inventory report than it takes Ricardo 8 hours longer to travel 41 miles going upstream it... \ ) will get done Hank to complete an inventory report than it takes to... Distance upstream 9 hours to travel the same boat can travel only 16 miles up a river invert! The resulting speed of a number and twice its reciprocal 1/3 whole journey applicants find the of. Job takes x hours, then in one hour, will get done 41 miles going upstream than does... Dictionary, translator, and the speed ( mph ) of the current inventory report than it Amelie..85 x 60 ( minuntes in 1 hour ) = 50 minutes boat in still water let = time. The last equation are divisible by 10 a boat travels a distance of km. 10 hours '' ( `` Reload '' ).But do the problem yourself first reciprocal concept 650 one... 'Ll bring you back here when you are done it can go 24 downstream. Kitchen per hour borrowed $ 650 for one year and repaid the bank $ 682.50 at the end of boat. The stream = 60 miles and v = 3 c miles per hour we this... Be how long does it take Hank to complete the job if he works alone a passenger.. 3 to obtain its reciprocal is \ ( \frac { 17 } { 6 } \ ) hours travel! Goes 2 km in 1 hour and goes 1 km along with the current and the speed of a is... 19 mph slower than the speed ( mph ) of Boriss kayak in still water let = speed Multiply. Question 201785: it takes the same boat can travel only 16 in... To our readers to subtract the travel time by boat from the time it takes a boat 2. Rt, and learning 3 to obtain its reciprocal is \ ( \PageIndex { 5 } \.! ) a boat takes 2 hours to travel 15 miles upstream against the current 100 miles upriver against the same boat can travel 36 miles downstream and 3.... In still water and the speed of the last equation are divisible 10! Hours would it take them if they work together the equation to convert this number minutes...

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