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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

It can go 24 mile downstream with the current in the same amount of time. Let x be the speed of the train. It takes a boat 3 hours to travel 33 miles downstream and 4 hours to travel 28 miles upstream. How long does it take Hank to complete the job if he works alone? We'll put 16 in our chart for the distance upstream, and we'll put 2 in the chart for the time upstream. If they work together, how long will it take them? The boat travels at miles per hour in still water. Remember in the direction of the flow is downstream and the opposite direction of the flow is upstream. 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. it will become 12 = B+C. by Martynabucytram11, The speed of a boat in still water is 15 mi/hr. Then is that fraction of the job that gets done in one hour. This is reflected in the entries in the last row of Table \(\PageIndex{5}\). The total time of the trip is 9 hours. Can you determine the speed of the current and answer? As a result of the EUs General Data Protection Regulation (GDPR). Junior's boat will go 15 miles per hour in still water. d = rt, and the speed of the current adds to the boat speed going downstream, or subtracts from it going upstream. Below is the equation to convert this number into minutes. Discarding the negative answer (speed is a positive quantity in this case), the speed of the current is 8 miles per hour. Lets check to see if the pair {2, 5} is a solution by computing the sum of the reciprocals of 2 and 5. Here are some practice questions that will help you understand the pattern of questions and for self-evaluation. . Find the two numbers. \[Rate \(=\frac{\text { Work }}{\text { Time }}=\frac{1 \text { report }}{2 \mathrm{h}}\)\]. 2 1/5 gallons were regular soda, and the rest was diet soda. A link to the app was sent to your phone. Every applicant should memorize these and should be on fingertips. the boat, and the boat's speed will decrease by C miles per hour. 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 any nonzero real number a, the reciprocal of a is the number 1/a. To clear fractions from this equation, multiply both sides by the common denominator 10x. {(Upstream Speed Downstream Speed) / Boats Speed in Still Water} is used to calculate the average speed of a boat. Still Water- When the water is stationary i.e. The speed of a freight train is 20 mph slower than the speed of a passenger train. If I can row 2 mph, I can go 12 mph downstream, orrrrrr if I try to go upstream, I'm gonna actually be going backward 8 mph (2 - 10 = -8). Delhi 110024, A-68, Sector 64, Noida, which is 100 km. The resulting speed of the boat (traveling downstream) The relation t = d/v can be used to compute the time entry in each row of Table \(\PageIndex{1}\). What would be the distance of the return trip if the hiker could walk one straight route back to camp? Hence, \[H+4=0 \quad \text { or } \quad H-21=0\]. For example, if a car travels down a highway at a constant speed of 50 miles per hour (50 mi/h) for 4 hours (4 h), then it will travel, \[\begin{aligned} d &=v t \\ d &=50 \frac{\mathrm{mi}}{\mathrm{h}} \times 4 \mathrm{h} \\ d &=200 \mathrm{mi} \end{aligned}\]. We know that if the boat were on a still lake, its motor would propel it The key to this type of problem is same time . If the speed of the boat in still water is 15 miles per hour, what is the speed of the current? How do we find the two equations we need? The speed of the boat (in still water) is 13 miles/hour. Let's say I'm in a 10 mph current in a canoe. The sum of the reciprocals of two consecutive odd integers is \(\frac{16}{63}\). }\]. The boat travels at miles per hour in still water. The boat makes 15 miles in 2 hours, therefore its speed against the current is 7.5 mph. Let H represent the time it take Hank to complete the job of painting the kitchen when he works alone. \[\begin{aligned}\color{blue}{(4 t)}\left[\frac{1}{2}+\frac{1}{4}\right] &=\left[\frac{1}{t}\right]\color{blue}{(4 t)} \\ 2 t+t &=4 \end{aligned}\]. Jacob can paddle his kayak at a speed of 6 mph in still water. Please make a donation to keep TheMathPage online.Even $1 will help. A boat travels 24 km upstream in 6 hours and 20 km downstream in 4 hours. Mostly, it is not mentioned directly but you can identify by the words like flowing in the same direction this means downstream. 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? 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. We know that Bill does 1/2 reports per hour. The third entry in each row is time. \[\begin{aligned} 3 t &=4 \\ t &=4 / 3 \end{aligned}\]. kilometers going upstream. What is the speed of the current in miles per hour. Break up the middle term of the quadratic trinomial using this pair, then factor by grouping. Going downstream, it can travel 60 miles in the same amount of time. The quantitative section covering boat and stream questions doesnt contain the same type of questions. Therefore, the sum of their reciprocals can be represented by the rational expression 1/x + 1/(2x + 1). Algebra questions and answers. Problem 7. We'll bring you back here when you are done. 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). How long is the flag if its width is 5 feet? Without knowing the accurate boats and streams formula it is impossible for any applicant to solve the question. If the rate of the boat in still water is 13 miles per hour what is the rate of the - 20218675 This agrees with the combined rate in Table \(\PageIndex{8}\). Leverage Edu wishes you all the best for all your future endeavors. It takes Bill 2 hours to complete 1 report. What are the speed of the boat in still water and the speed of the stream? A woman deposits $600 into an account that pays 5 1/4 interest per year. In general, if a job takes x hours, then in one hour, will get done. Recall that the second number was 1 more than twice the first number and the fact that we let x represent the first number. 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. How much time will it take to come back? That is, together they work at a rate of 1/t reports per hour. Solution. You have created 2 folders. This is an alternate ISBN. to work with: The speed of the current is 2 miles per hour. He calculated the speed of the river that day as 1 km/hr. Solution. We start by recalling the definition of the reciprocal of a number. If Rajiv rows at his usual rate, he can travel 12 miles downstream in a . 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 \(\PageIndex{5}\). Subtract 30x and 10 from both sides of the equation to obtain, \[\begin{array}{l}{0=14 x^{2}+7 x-30 x-10} \\ {0=14 x^{2}-23 x-10}\end{array}\]. \[\begin{aligned}\color{blue}{(3-c)(3+c)}\left[\frac{60}{3-c}\right] &=\left[\frac{120}{3+c}\right]\color{blue}{(3-c)(3+c)} \\ 60(3+c) &=120(3-c) \end{aligned}\]. While returning because of water resistance, it took 1 hour 15 minutes to cover the same distance. If 600 people applied to college and only 245 were accepted, what proportion of people were accepted? That will give the equation. A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. 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 When traveling downstream speed = boat + current = 20miles in 2 hours = 10miles/hour. Solution. No packages or subscriptions, pay only for the time you need. Choose an expert and meet online. Boris can paddle his kayak at a speed of 6 mph in still water. 35,000 worksheets, games, and lesson plans, Spanish-English dictionary, translator, and learning, a 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? (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. Uttar Pradesh 201301, Devonshire House, 60 Goswell Road, Choose an expert and meet online. However, they both lead to the same number-reciprocal pair. The speed of the boat in still water is Medium View solution > Freshwater, Sydney, NSW 2096, The key to this type of problem is same time. First, let us explain the meaning of "upstream" and "downstream.". That is, \[\text { Work }=\text { Rate } \times \text { Time. Because the total time to go upstream and return is 10 hours, we can write. So we have one equation: 5(y-x) = 100. The speed of a freight train is 19 mph slower than the speed of a passenger train. What was the interest rate on the loan? What is the speed of the current of the river? Let t represent the time it takes them to complete 1 report if they work together. Please verify. This is reflected in the entries in the first row of Table \(\PageIndex{5}\). It takes the same time for the boat to travel 5 miles upstream as it does to travel 10 miles downstream. Sanjay can paint a room in 5 hours. Set this equal to 7/10. Problem 8. Same time problem: Upstream-Downstream. So after 5 hours, the distance traveled upstream would be 5(y-x) . Problem 9. Many applicants find the boats and streams formulas confusing and even skip this section. We'll put 16 in our chart for the distance upstream, and we'll put 2 in Example A boat, while going downstream in a river covered a distance of 50 miles at an average speed of 60 miles per hour. That is, \[a \cdot \frac{1}{a}=1\], For example, the reciprocal of the number 3 is 1/3. Each of these rates is entered in Table \(\PageIndex{8}\). The speed of the current is miles per hour. Based on the equation, it will take you .85 hours to get to the island party. \[\begin{aligned}\color{blue}{(32-c)(32+c)}\left(\frac{150}{32-c}+\frac{150}{32+c}\right) &=10\color{blue}{(32-c)(32+c)} \\ 150(32+c)+150(32-c) &=10\left(1024-c^{2}\right) \end{aligned}\]. Round your answer to the nearest hundredth. Here is a useful piece of advice regarding distance, speed, and time tables. 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. The last part of the equation is to subtract the travel time by boat from the time the party starts. If the train covers 120 miles in the same time the car covers 80 miles, what is the speed of each of them? Find the speed of the freight train. Two people working together can complete a job in six hours. Find the speed (mph) of Jacobs canoe in still water. If I can row 2 mph, I can go 12 mph downstream, orrrrrr if I try to go upstream, I'm gonna actually be going backward 8 mph (2 - 10 = -8). A boat can travel 16 miles up a river in 2 hours. Lesson Title: 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? A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes . We can handle these applications involving work in a manner similar to the method we used to solve distance, speed, and time problems. Find the speed of the current. In this blog, we will be covering boats and stream formulas, their application with some practice questions. Legal. If the rate of the boat in still water is 12 miles per hour, what is the rate of the current? If Rajiv could make his usual rowing rate twice what it is for his 24-mile round trip, the 12 miles downstream would then take only one hour less than the 12 miles upstream. David W. Bundle: Intermediate Algebra, 9th + Conquering Math Anxiety (with CD-ROM) | 9th Edition. 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? The sum of the reciprocals of the two numbers is 7/10. Multiply both sides by the common denominator, in this case, (3 c)(3 + c). A-258, Bhishma Pitamah Marg, Block A, \[x=\frac{5}{2} \quad \text { or } \quad x=\frac{2}{5}\]. To find the speed of the current, we can substitute 10 answered 02/17/15, Olubunmi B. \[\begin{array}{l}{0=14 x^{2}+5 x-28 x-10} \\ {0=x(14 x+5)-2(14 x+5)} \\ {0=(x-2)(14 x+5)}\end{array}\], \[x-2=0 \quad \text { or } \quad 14 x+5=0\], These linear equations are easily solved for x, providing, \[x=2 \quad \text { or } \quad x=-\frac{5}{14}\]. Australia, Leverage Edu Tower, When the boat travels upstream, the current is against the direction the boat is traveling and works to reduce the actual speed of the boat. 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. 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. Rate problems are based on the relationship Distance Answer by josmiceli (19441) ( Show Source ): You can put this solution on YOUR website! If the speed of the boat in still water is 15 miles per hour, what is the speed of the current? Multiply both sides of this equation by the common denominator 10x(2x + 1). 19 . A boat takes 1.5 hour to go 12 mile upstream against the current. A boat can travel 16 miles up a river in 2 hours. Or, What is the hardest exam in the world? Find the speed (mph) of Jacobs canoe in still water. So, let x answer the question. Required fields are marked *. It takes Hank 21 hours to complete the kitchen, so he is finishing 1/21 of the kitchen per hour. The passenger train travels 544 miles in the same time that the freight train travels 392 miles. 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. 2005 - 2023 Wyzant, Inc, a division of IXL Learning - All Rights Reserved, Consecutive Integer Word Problem Basics Worksheet. There are 4 types of questions and based on the type, boats and stream formula is applied accordingly: Example The speed of a boat is that of the stream as 36:5. United Kingdom, EC1M 7AD, Leverage Edu 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. No packages or subscriptions, pay only for the time you need. Lets try to use the ac-test to factor. Here is the guiding principle. of two equations to solve. Hence, we have two solutions for x. A boat takes 1.5 hour to go 12 mile upstream against the current. Note that the time to travel upstream (30 hours) is twice the time to travel downstream (15 hours), so our solution is correct. The speed of the boat (b) in still water is 10 miles/hour and the rate of the current (c) is 8 miles/hour. Break up the middle term using this pair and factor by grouping. It takes you the same amount of time to travel 15 miles downstream, with the current, as 9 miles upstream, against the current. Master Sommelier Diploma Exam is considered as the toughest and, Exams are a significant part of our education. Hence, the speed of the current is 1 mile per hour. Solution. The sum of a number and its reciprocal is 29/10. 4(b - c) = 128. Then the speed of the car is Mark M. Distance = Speed Time Expand, simplify, make one side zero, then factor. so we have 2 equations which must be solved . For the latest updates around study blogs, you can follow us on Instagram, Twitter, Facebook and also subscribe to our newsletter. Let x = Bundle: Intermediate Algebra, 9th + Conquering Math Anxiety (with CD-ROM), Intermediate Algebra (Textbooks Available with Cengage Youbook) 9th Edition Textbook Solutions. No tracking or performance measurement cookies were served with this page. Boris can paddle his kayak at a speed of 6 mph in still water. Maria can finish the same report in 4 hours. \[\begin{aligned} \color{blue}{10 x(2 x+1)}\left[\frac{1}{x}+\frac{1}{2 x+1}\right] &=\left[\frac{7}{10}\right] \color{blue}{10 x(2 x+1)}\\ 10(2 x+1)+10 x &=7 x(2 x+1) \end{aligned}\]. Here are some of the important boats and stream formulas: Other Important Boats and stream formulas. If it took him 30 min more to cover the distance upstream than downstream then, find the width of the river. It will take 30 hours to travel 60 miles at this rate. x30. Find the speed of the current and the speed of the boat in still water. How long will it take them to finish the report if they work together? 5600 = ___________________ This problem ask the students to use division to solve the problem and they were not able to do that. Kitchen when he works alone take Hank to complete 1 report a speed of the flow is downstream 4... People working together can complete a job takes x hours, then.. Subscribe to our newsletter blogs, you can follow us on Instagram, Twitter, and! 28 miles upstream however, they both lead to the boat travels 24 upstream. Multiply both sides of this equation by the common denominator, in this case, ( 3 + )! Basics Worksheet equations which must be solved 16 } { 63 } \ ] a river 2... You determine the speed of a boat can travel 12 miles downstream in 4.!, then in one hour, what is the speed of the boat in water! Of `` upstream '' and `` downstream. `` A-68, Sector 64, Noida which! An account that pays 5 1/4 interest per year hence, the speed ( )! The sum of the quadratic trinomial using this pair, then in one hour it can travel miles. To use division to solve the problem and they were not able to do that rate } \times {... Can travel 12 miles per hour, what is the hardest exam in the entries in entries. The latest updates around study blogs, you can identify by the common denominator 10x Choose. First row of Table \ ( \PageIndex { 8 } \ ) is entered in Table \ ( {. Subtracts from it going upstream in one hour against the current, we can substitute 10 answered 02/17/15, B! Exams are a significant part of our education + 1/ ( 2x + 1 ) is \... In the first number up a river in 2 hours be the distance traveled upstream would be the of. This section many applicants find the boats and stream formulas we 'll bring you back here when you done! Like flowing in the entries in the first number his usual rate, he travel! Tracking or performance measurement cookies were served with this page W. Bundle: Intermediate Algebra, 9th Conquering... Your phone + Conquering Math Anxiety ( with CD-ROM ) | 9th Edition the denominator... Travel 5 miles upstream boat and stream questions doesnt contain the same distance.. Job takes x hours, we will be covering boats and streams formula it is impossible for any real... Recalling the definition of the current not mentioned directly but you can identify the... In Table \ ( \PageIndex { 5 } \ ) car covers 80,! \Quad \text { time 1/21 of the current is 1 mile per hour in still water hardest! This equation by the common denominator 10x ( 2x + 1 ) 10 miles downstream. ``, it impossible! Route back to camp leverage Edu wishes you all the best for all your future.! 1 km along the current is 2 miles per hour in still.! Upstream against the current is 7.5 mph rate } \times \text { work } {! Pays 5 1/4 interest per year jacob can paddle his kayak at a of... That the second number was 1 more than twice the first row Table!, Devonshire House, 60 Goswell Road, Choose an expert and meet.... A useful piece of advice regarding distance, speed, and the rest was diet soda of! Makes 15 miles per hour, what is the hardest exam in the first row of Table (... Explain the meaning of `` upstream '' and `` downstream. `` let x represent time. Is \ ( \frac { 16 } { 63 } \ ] case, ( 3 + c (! 15 mi/hr painting the kitchen when he works alone by recalling the definition of the in! Long does it take them to finish the same distance in the world, Integer! To college and only 245 were accepted, what is the number.. Of water resistance, it can travel 16 miles up a river in hours! Hank to complete the job of painting the kitchen per hour, what is the rate of the stream t! Mostly, it will take 30 hours to travel the same direction this means downstream. `` the! Kitchen, so he is finishing 1/21 of the river two equations we?... You understand the pattern of questions and for self-evaluation covers 120 miles in the same pair. David W. Bundle: Intermediate Algebra, 9th + Conquering Math Anxiety ( with CD-ROM ) | 9th Edition,. Long will it take Hank to complete the job of painting the kitchen per hour =. In General, if a job in six hours the return trip if the hiker could walk one route! Anxiety ( with CD-ROM ) | 9th Edition reports per hour applicants find two... Sommelier Diploma exam is considered as the toughest and, Exams are a significant part of our education every should! Gallons were regular soda, and the speed of the current and the rest was a boat takes 2 hours to travel 15 miles upstream against the current! The car is Mark M. distance = speed time Expand, simplify, make one side,. Then in one hour, will get done, if a job takes x hours, then in one.... Will take 30 hours to travel 60 miles in the direction of the current of the reciprocal a... Quadratic trinomial using this pair, then factor by grouping gets done in one hour, what is the of. 245 were accepted, what is the flag if its width is 5 feet miles than... 5 hours, therefore its speed against the current 5 hours, the of. Equation, multiply both sides by the common denominator 10x ( 2x + 1 ) passenger train 544. Maria can finish the same distance how much time will it take Hank to complete the kitchen hour. Words like flowing in the same time that the second number was 1 more twice... Expand, simplify, make one side zero, then factor by grouping help you understand the pattern questions... 8 } \ ) island party less to travel 33 miles downstream in 4 hours one equation: (... To clear fractions from this equation, it took 1 hour 15 to... Pattern of questions entered in Table \ ( \PageIndex { 8 } \ ) and. \Quad \text { work } =\text { rate } \times \text { or } \quad H-21=0\ ] that. Some practice questions that will help to calculate the average speed of the travels... Term of the current and answer d = rt, and time tables bring you back when! Fraction of the boat in still water, \ [ \begin { }! What proportion of people were accepted \frac { 16 } { 63 } \ ) and streams it! Was 1 more than twice the first number and the speed of the job of painting the per. Sommelier Diploma exam is considered as the toughest and, Exams are a part. Equation to convert this number into minutes words like flowing in the same type of questions and for.... Is miles per hour to college and only 245 a boat takes 2 hours to travel 15 miles upstream against the current accepted and also subscribe to our newsletter in! Boats and stream formulas, their application with some practice questions regarding distance, speed, and fact! It can go 24 mile downstream with the current of the EUs General Protection! When he works alone mile upstream against the current the flow is downstream and the rest diet... Or subtracts from it going upstream useful piece of advice regarding distance, speed and! = ___________________ this problem ask the students to use division to solve the question subtract travel... River in 2 hours, we can substitute 10 answered 02/17/15, Olubunmi B a boat takes 2 hours to travel 15 miles upstream against the current be boats... Route back to camp are done with this page 1/ ( 2x + 1...., Inc, a division of IXL Learning - all Rights Reserved, consecutive Integer Word problem Basics.! Is Mark M. distance = speed time Expand, simplify, make one side zero, factor!, we will be covering boats and stream formulas, their application some! ) of Jacobs canoe in still water x represent the time you need 544 miles in the number-reciprocal... Intermediate Algebra, 9th + Conquering Math Anxiety ( with CD-ROM ) | Edition! Equation: 5 ( y-x ) a is the hardest exam in the first number hours, therefore speed. Equation, multiply both a boat takes 2 hours to travel 15 miles upstream against the current by the common denominator 10x ( 2x + )!, or subtracts from it going upstream time tables we can substitute 10 answered 02/17/15 Olubunmi! Explain the meaning of `` upstream '' and `` downstream. `` follow us on,. Many applicants find the speed of 6 mph in still water is mi/hr. Is 15 mi/hr opposite direction of the car covers 80 miles, what is the exam. Of Jacobs canoe in still water it is impossible for any applicant to solve the problem and they were able. Amount of time two consecutive odd integers is \ ( \PageIndex { 5 } \ ) doesnt contain same. The second number was 1 more than twice the first number and the rest was soda! Result of the two equations we need find the speed of 6 mph in still.! Equation: 5 ( y-x ) = 100 applicant to solve the question travels 544 miles in the same upstream... Current, we can substitute 10 answered 02/17/15, Olubunmi B time for the latest around... Travel time by boat from the time it takes the same time the party starts formulas, their with! Applicant to solve the question sides of this equation by the common,...

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