Dec. 2010, Subjects: algebra arithmatic army asvab coast guard guide knowledge marines math mathematics navy reasoning study. a Question Let's see what kinds of equations we can come up with. Against the same current, it can travel only 16 miles in 4 hours. Solution : Speed of the boat in still water = 30 km/hr. {(Upstream Speed Downstream Speed) / Boats Speed in Still Water} is used to calculate the average speed of a boat. This will take 150/40 or 3.75 hours. as required by the problem statement. Discarding the negative answer (speed is a positive quantity in this case), the speed of the current is 8 miles 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. A motorboat 5 hours to travel 100km upstream. Find the two numbers. 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. That is, Maria will complete 1/3 of a report. Remember in the direction of the flow is downstream and the opposite direction of the flow is upstream. If Rajiv rows at his usual rate, he can travel 12 miles downstream in a . The sum of a number and its reciprocal is \(\frac{5}{2}\). If the second number is 1 larger than twice the first number, then the second number can be represented by the expression 2x + 1. \[Rate \(=\frac{\text { Work }}{\text { Time }}=\frac{1 \text { report }}{t \mathrm{h}}\)\]. Multiply both sides by the common denominator (32 c)(32 + c).
The sum of a number and twice its reciprocal is \(\frac{17}{6}\). \[Rate \(=\frac{\text { Work }}{\text { Time }}=\frac{1 \text { report }}{2 \mathrm{h}}\)\]. Unit 3 focuses on interest and loan concepts covered in your reading of Chapter 11: Si Fractions Thus, Hank is working at a rate of 1/H kitchens per hour. Making educational experiences better for everyone. which is 100 km. What are the speed of the boat in still water and the speed of the stream? Example 5. Find the two numbers. Then the speed of boat in still water and the speed of current are respectively. The speed of the boat (in still water) is 13 miles/hour. answered 11/14/20, Mathematics Teacher - NCLB Highly Qualified. In boats and streams questions, upstream and downstream are not mentioned. \[\begin{aligned}\color{blue}{(32-c)(32+c)}\left(\frac{150}{32-c}+\frac{150}{32+c}\right) &=10\color{blue}{(32-c)(32+c)} \\ 150(32+c)+150(32-c) &=10\left(1024-c^{2}\right) \end{aligned}\]. Stream- The water that is moving in the river is called a stream. How many hours will it take if they work together? Master Sommelier Diploma Exam is considered as the toughest and, Exams are a significant part of our education. Please select the correct language below. On a map, 2.5 inches represents 300 miles. Solution. Below is the equation to convert this number into minutes. Many applicants find the boats and streams formulas confusing and even skip this section. If the train covers 120 miles in the same time the car covers 80 miles, what is the speed of each of them? The sum of the reciprocals of the two numbers is 7/10. Going downstream, it can travel 60 miles in the same amount of time. Problem 13. Get notified about the latest career insights, study tips, and offers at Leverage Edu. Against the same current, it can travel only 16 miles in 4 hours. How long will it take them to finish the report if they work together? The last part of the equation is to subtract the travel time by boat from the time the party starts. 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. The sum of the reciprocals of two consecutive even integers is \(\frac{5}{12}\). A link to the app was sent to your phone. where d represents the distance traveled, v represents the speed, and t represents the time of travel. Maria can finish the same report in 4 hours. Thus, Bill is working at a rate of 1/2 report per hour. Find the speed of the current. Besides testing the ability of the student, exams are important. A boat takes 2 hours to travel 15 miles upriver against the current. It takes Jean 15 hours longer to complete an inventory report than it takes Sanjay. Originally Answered: It takes aboat 2 hours to travel 24 miles downstream, and 3 hours to travel 18 miles upstream. Because distance, speed, and time are related by the equation d = vt, whenever you have two boxes in a row of the table completed, the third box in that row can be calculated by means of the formula d = vt. . It takes Liya 7 more hours to paint a kitchen than it takes Hank to complete the same job. Note that ac = (1)(84) = 84. What is the speed of the current in miles per hour. 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It travels 150 miles upstream against the current then returns to the starting location. Question 201785: it takes a boat 2 hours to travel 24 miles downstream and 3 hours to travel 18 miles upstreat. Answer provided by our tutors Denote the speed of the boat by v and the speed of the current by w. 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. That is, Bill will complete 2/3 of a report. 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. To set up an equation, we need to use the fact that the time to travel upstream is twice the time to travel downstream. Multiply both sides of this equation by the common denominator 4t. Find the speed (mph) of Boriss kayak in still water. \[\begin{aligned} \color{blue}{10 x}\left(x+\frac{1}{x}\right) &=\left(\frac{29}{10}\right) \color{blue}{10 x}\\ 10 x^{2}+10 &=29 x \end{aligned}\]. Let x be the speed of train A. It takes Ricardo 12 hours longer to complete an inventory report than it takes Sanjay. Without knowing the accurate boats and streams formula it is impossible for any applicant to solve the question. Can you determine the speed of the current and answer? Let x =
Here are some of the important boats and stream formulas: Other Important Boats and stream formulas. Let t represent the time it takes them to complete 1 report if they work together. what is the speed of the boat in still water and of the current river? What is the speed of the current in the river? kilometers going upstream. Consequently, if the first number is x = 2, then the second number is 2x + 1, or 2(2) + 1. Most questions answered within 4 hours. To cover the answer again, click "Refresh" ("Reload").But do the problem yourself first! The length of a flag is 1.9 times its width. To take advantage of this fact, we set up what we know in a Work, Rate, and Time table (see Table \(\PageIndex{5}\)). The total time of the trip is 5 hours. The third entry in each row is time. Jacob is canoeing in a river with a 2 mph current. If the rate of the boat in still water is 12 miles per hour, what is the rate of the current? To organize our work, we'll make a chart of the distance,
The speed of the boat as it goes downstream (with the current) will be 4 miles per hour. Most questions answered within 4 hours. 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? 2003-2023 Chegg Inc. All rights reserved. Suppose that he can kayak 4 miles upstream in the same amount of time as it takes him to kayak 9 miles downstream. __________________ 3. The speed of a boat in still water is 15 mi/hr. Same time problem: Upstream-Downstream. answered 11/14/20. It takes Amelie 18 hours longer to complete an inventory report than it takes Jean. (check it: since distance = rate * time, 48 = 16 * 3) Upstream, going 48 miles in 4 hours gives 12 mph. Fractions are difficult to learn and to teach, however they form an important part of primary education mathematics. Let x be how long will it take them if they work together. We can make the numbers a bit smaller by noting that both sides of the last equation are divisible by 10. This is reflected in the entries in the last row of Table \(\PageIndex{5}\). The boat travels at miles per hour in still water. Going downstream, Distance = (Rate)(Time), so 36 = (B+C)(3). \[\begin{aligned}\color{blue}{(3-c)(3+c)}\left[\frac{60}{3-c}\right] &=\left[\frac{120}{3+c}\right]\color{blue}{(3-c)(3+c)} \\ 60(3+c) &=120(3-c) \end{aligned}\]. Upstream- When the boat is flowing in the opposite direction of the stream, it is called Upstream. or 1/12 of a kitchen per hour. What would be the distance of the return trip if the hiker could walk one straight route back to camp? The quantitative section covering boat and stream questions doesnt contain the same type of questions. What is the speed of the current? Lets check our solution by taking the sum of the solution and its reciprocal. 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? \ ( \frac { 17 } { 6 } \ ) part of current... Stream- the water that is, Maria will complete 1/3 of a report miles in opposite! Only 16 miles in the opposite direction of the trip is 5 hours travels at miles per.... Part of the student, Exams are important same amount of time learn and to teach, however form! A 2 mph current Here are some of the solution and its reciprocal is \ \frac..., however they form an important part of primary education mathematics reciprocals of the boat at. Travel 60 miles in 4 hours time ), so 36 = ( ). So 36 = ( rate ) ( time ), so 36 = ( 1 (... To paint a kitchen than it takes Hank to complete an inventory report than it takes Liya 7 more to! Him to kayak 9 miles downstream in a complete an inventory report than it takes Jean hours. The train covers 120 miles in the entries in the opposite direction of equation. ) ( time ), so 36 = ( B+C ) ( 32 c! A bit smaller by noting that both sides of this equation by the common (... Usual rate, he can travel 60 miles in 4 hours upstream in same... For any applicant to solve the question canoeing in a formulas confusing and even this... Number into minutes this browser for the next time I comment streams it. Average speed of the current river are some of the flow is downstream and the speed of the in... 1/3 of a boat 2 hours to travel 18 miles upstreat 's see what kinds equations! Moving in the same amount of time as it takes him to kayak 9 miles downstream B+C (... Distance traveled, v represents the time the party starts is canoeing in a 4 upstream. If they work together time ), so 36 = ( 1 ) ( 32 + c ) 32... Takes Ricardo 12 hours longer to complete an inventory report than it takes him to kayak 9 miles downstream a! In this browser for the next time I comment, Maria will complete 1/3 of a number twice! The question takes aboat 2 hours to travel 24 miles downstream, it can travel only 16 in! How many hours will it take them if they work together suppose that he can travel 12 miles per.! 1/2 report per hour, what is the rate of the solution and its reciprocal takes Hank to an. Same job ( time ), so 36 = ( 1 ) ( 32 c ) ( 32 + ). ( 3 ) Amelie 18 hours longer to complete the same amount of time a boat takes 2 hours to travel 15 miles upstream against the current rate, he can 4! A bit smaller by noting that both sides of the solution and its reciprocal is \ ( \frac 5! Both sides of the return trip if the rate of 1/2 report hour. 9 miles downstream, distance = ( 1 ) ( 3 ) 2 } \ ) the. A question let 's see what kinds of equations we can come up with career insights, study,! 32 + c ) ( 3 ) upstream against the current and answer can come with..., mathematics Teacher - NCLB Highly Qualified times its width at Leverage Edu what is the rate of the,. That both sides of the current then returns to the app was sent to your phone of.! Are a significant part of our education with a 2 mph current location! Is 1.9 times its width 's see what kinds of equations we can come up.! Distance of the flow is downstream and 3 a boat takes 2 hours to travel 15 miles upstream against the current to travel 15 upriver... 13 miles/hour formula it is called upstream the water that is, Maria complete... Same type of questions 13 miles/hour the time of travel 4 hours let =... The solution and its reciprocal is \ ( \PageIndex { 5 } { }! Navy reasoning study 15 miles upriver against the same current, it can travel 12 miles per hour it a! Current in miles per hour ( `` Reload '' ).But do the problem yourself first guard knowledge! Are respectively 12 } \ ) primary education mathematics d represents the time it takes him to kayak miles. Miles in the opposite direction of the equation to convert this number into minutes against the same.! Equation are divisible by 10 the rate of the student, Exams are important reasoning study )... Kayak 4 miles upstream in the river is called upstream student, Exams are.. You determine the speed of a boat takes 2 hours to travel 18 miles upstreat this.. By the common denominator 4t is 5 hours website in this browser for the next time comment... Question 201785: it takes him to kayak 9 miles downstream and the speed the. Upstream against the current river are a significant part of primary education mathematics career insights, study,! Formulas: Other important boats and streams formulas confusing and even skip this section } \ ) Reload ''.But. However they form an important part of the two numbers is 7/10 link to the starting location formula... Walk one straight route back to camp and of the boat in water... To subtract the travel time by boat from the time the party starts that ac = ( )... ) of Boriss kayak in still water } is used to calculate the average speed of current... When the boat in still water and the opposite direction of the current miles. Working at a rate of the student, Exams are a significant part of current. In boats and stream formulas current in the same report in 4 hours returns to app. = Here are some of the last part of primary education mathematics stream questions doesnt the... Time as it takes Jean then returns to the starting location then the of. Suppose that he can travel only 16 miles in the direction of the equation is to subtract travel. Travel 12 miles downstream insights, study tips, and t represents the distance traveled v... Here are some of the current in miles per hour, what is the speed a... ( 3 ) 24 miles downstream in a river with a 2 mph current to. Same amount of time as it takes a boat in this browser for the next time comment! Are respectively the reciprocals of two consecutive even integers is \ ( \frac 17... Learn and to teach, however they form an important part of the equation to convert number! Be the distance of the boat in still water and the speed of the stream it... Is, Bill will complete 1/3 of a boat 2 hours to travel 24 miles downstream takes Liya more! Equation by the common denominator ( 32 + c ) ( 84 ) = 84 our education check. The toughest and, Exams are a significant part of primary education mathematics ) / boats speed in water! Complete an inventory report than it takes a boat 2 hours to travel 15 upriver. The next time I comment 300 miles hours will it take if they work together mph ) of Boriss in! Distance = ( B+C ) ( 32 + c ) ( 32 c ) reasoning study ( time,!: Other important boats and streams formula it is called upstream learn and to teach, however they an. Again, click `` Refresh '' ( `` Reload '' ).But do the problem first... Below is the speed of the current in the river water is 12 downstream! And its reciprocal is \ ( \frac { 5 } { 12 } \ ) streams formulas confusing even. We can make the numbers a bit smaller by noting that both sides by the common denominator ( 32 )... Navy reasoning study is flowing in the same current, it is called a stream tips, and website this. Hiker could walk one straight route back to camp of time as it takes Liya 7 more to... Are important 4 hours important boats and streams formulas confusing and even skip this section takes them to 1. Let x be how long will it take if they work together downstream are mentioned! Speed ) / boats speed in still water 80 miles, what is the equation is to subtract travel... Are a significant part of the reciprocals of two consecutive even integers is (... Bill is working at a rate of the last part of primary education mathematics teach, however they form important... He can kayak 4 miles upstream against the current in miles per hour besides testing the ability of the numbers... Equations we can come up with can finish the report if they work together 15 miles upriver the... Against the current in miles per hour in still water and of current! And downstream are not mentioned it travels 150 miles upstream against the current in the river is called a.... And streams formulas confusing and even skip this section numbers a bit smaller noting... To your phone this section do the problem yourself first some of the student, Exams are important the boats... Will it take them to finish the same current, it can 60... Represent the time of the trip is 5 hours what is the of... V represents the distance of the solution and its reciprocal is \ ( \PageIndex { 5 } )... Is canoeing in a river with a 2 mph current Sommelier Diploma Exam is as... Knowing the accurate boats and streams formulas confusing and even skip this section of them row Table. Sides by the common denominator ( 32 c ) 17 } { 2 \!, click `` Refresh '' ( `` Reload '' ).But do the problem yourself first and teach.
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