How many miles are represented by 6 inches? Against the same current, it can travel only 16 miles in 4 hours. Hence, the pair {14/5, 7/2} is also a solution. Break up the middle term of the quadratic trinomial using this pair, then factor by grouping. A club has 4 Blue kites, 3 Green kites, and 3 Yellow kites. : 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 This equation is linear (no power of t other than 1) and is easily solved. ---------------- Downstream DATA: 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 \(\PageIndex{7}\). The key to this type of problem is: What fraction of the job gets done in one hour? How tall is the tower? Thus, our two numbers are x and 2x+1. A woman deposits $600 into an account that pays 5 1/4 interest per year. Find the number(s). In general, if a job takes x hours, then in one hour, will get done. Example The speed of the boat when traveling downstream is 32 km/hr. That is, \[a \cdot \frac{1}{a}=1\], For example, the reciprocal of the number 3 is 1/3. Your contact details will not be published. There are two numbers. If the speed of the boat in still water is 15 miles per hour, what is the speed of the current? An OTP has been sent to your registered mobile no. The same boat can travel 36 miles downstream in 3 hours. Hence, we want to isolate all terms containing c on one side of the equation. What is the speed of the current? Round your answer to the nearest hundredth. Uttar Pradesh 201301, Devonshire House, 60 Goswell Road, Please verify. As a result of the EUs General Data Protection Regulation (GDPR). What is the speed of the current of the river? Here is a useful piece of advice regarding distance, speed, and time tables. It takes Amelie 18 hours longer to complete an inventory report than it takes Jean. 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. The current speed . Our team will review it before it's shown to our readers. Find the speed of the freight train. Our chart now looks like . If the second number is 1 larger than twice the first number, then the second number can be represented by the expression 2x + 1. For the latest updates around study blogs, you can follow us on Instagram, Twitter, Facebook and also subscribe to our newsletter. Here are the important terms every applicant should know: Also Read: Permutation And Combination For Competitive Exams. To clear fractions from this equation, multiply both sides by the common denominator 10x. 35,000 worksheets, games, and lesson plans, Spanish-English dictionary, translator, and learning. The sum of the reciprocals of two consecutive even integers is \(\frac{5}{12}\). But the boat is not on a still lake; Here are some tips and tricks for boats and stream questions: Also Read: Tips to Crack Competitive Exams. d = rt, and the speed of the current adds to the boat speed going downstream, or subtracts from it going upstream. How far away was Boston? Upstream- When the boat is flowing in the opposite direction of the stream, it is called Upstream. so we have 2 equations which must be solved . On the other hand, if the boat is traveling downstream, the current will A boat can travel 24 miles in 3 hours when traveling with a current. Most questions answered within 4 hours. Therefore, The rate of current is, Hence, The required rate of current is 1.6. No packages or subscriptions, pay only for the time you need. That will give the equation, Time upstream = Time downstream Now, speed, or velocity, is distance divided by time -- so many miles per hour: Therefore, t = d v The equation will be Problem 5. __________________ 3. 1] . He paddles 5 miles upstream against the current and then returns to the starting location. Note that the right-hand side of this equation is quadratic with ac = (14)(10) = 140. Current It takes a boat 2 hours to travel 18 miles upstream against the current. When traveling downstream speed = boat + current = 20miles in 2 hours = 10miles/hour. A boat takes 1.5 hour to go 12 mile upstream against the current. Let t represent the time it takes them to complete 1 report if they work together. A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. whereas when traveling upstream it is 28 km/hr. A-258, Bhishma Pitamah Marg, Block A, That is, Bill will complete 2/3 of a report. What are we trying to find in this problem? It will take 15 hours to travel 60 miles at this rate. While returning because of water resistance, it took 1 hour 15 minutes to cover the same distance. We still need to answer the question, which was to find two numbers such that the sum of their reciprocals is 7/10. Can you determine the speed of the current and answer? Find out how you can intelligently organize your Flashcards. How long will it take them to finish the report if they work together? For Free. In boats and streams questions, upstream and downstream are not mentioned. We hope you liked this blog and will help you in preparing your speech on the Importance of English. 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? The resulting speed of the boat (traveling downstream) The speed of the current is 5 miles per hour. 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. This is reflected in the entries in the second row of Table \(\PageIndex{5}\). Using the equation speed = distance/time: 12 miles upstream take 1.5 hours, so v-w=12/1.5=24/3=8 m/h, 24 miles downstream take 1.5 hours as well, so v+w=24/1.5=48/3=18 m/h, Add them: v-w+v+w=8+18 ==> 2v=26 ==> v=13, Plug in one of the equations to get w: 13+w=18 ==> w=15. boat's average speed: 14 mph current speed: 2 mph going downstream, going 48 miles in 3 hours implies a speed of 16 miles each hour. where d represents the distance traveled, v represents the speed, and t represents the time of travel. 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). For example, in the first row, d = 60 miles and v = 3 c miles per hour. x30. 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. The arithmetic is easier in the second one, so: Go back to the original definitions of x and y to interpret the results. This result is also recorded in Table \(\PageIndex{6}\). He calculated the speed of the river that day as 1 km/hr. Together, they can complete the same job in 12 hours. The speed of a boat in still water is 15 mi/hr. What is the rate of water's current? \[Rate \(=\frac{\text { Work }}{\text { Time }}=\frac{1 \text { report }}{t \mathrm{h}}\)\]. document.getElementById( "ak_js_1" ).setAttribute( "value", ( new Date() ).getTime() ); 150 Common: Difficult Idioms with Examples. Problem 7. Break up the middle term using this pair and factor by grouping. It takes Ricardo 8 hours longer to complete an inventory report than it takes Amelie. After 6 hours, \[\text { Work }=3 \frac{\text { lawns }}{\mathrm{hr}} \times 6 \mathrm{hr}=18 \text { lawns. Also Read: A Guide On How to Prepare for Bank Exams. How many hours would it take Jean if she worked alone? However, the last row of Table \(\PageIndex{6}\) indicates that the combined rate is also 1/t reports per hour. If Rajiv rows at his usual rate, he can travel 12 miles downstream in a . answered 11/14/20. If the speed of the boat in still water is 10 mph, the speed of the stream is: 2 mph; 2.5 mph; 3 mph ; 4 mph; None of These; Answer: 2 mph . If we divide both sides of the first equation by 2, it It takes Hank 21 hours to complete the kitchen, so he is finishing 1/21 of the kitchen per hour. Katrina drove her car to Boston at a speed of 100 kph (kilometers per hour). Same time problem: Upstream-Downstream. A boat takes 2 hours to travel 15 miles upriver against the current. Requested URL: byjus.com/govt-exams/boat-stream-questions/, User-Agent: Mozilla/5.0 (Windows NT 6.3; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/103.0.0.0 Safari/537.36. }\], A second important concept is the fact that rates add. If 600 people applied to college and only 245 were accepted, what proportion of people were accepted? Let H represent the time it take Hank to complete the job of painting the kitchen when he works alone. 2 1/5 gallons were regular soda, and the rest was diet soda. What would be the distance of the return trip if the hiker could walk one straight route back to camp? Note that ac = (10)(10) = 100. It is important to check that the solution satisfies the constraints of the problem statement. Let x = The integer pair {5, 28} has product 140 and sum 23. Moira can paddle her kayak at a speed of 2 mph in still water. Example 3. A boat travels 30 miles downstream in 2 hours and it takes 4 hours to travel back upstream. Since we are told that in still water (no current), the boat would be making 12 mph, it follows therefore that the current's speed must be the difference of 12 - 7.5, or 4.5 mph. Hence, the sum of x and its reciprocal is represented by the rational expression x + 1/x. It takes Sanjay 7 hours to paint the same room. A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. An idiom is an expression or phrase whose meaning does not relate to the, 50 Difficult Words with Meanings. 2003-2023 Chegg Inc. All rights reserved. Example 5. Defence Colony, New Delhi, How many floor boards 2 1/4 inches wide are needed to cover a floor 15 feet wide? However, they both lead to the same number-reciprocal pair. The speed of a freight train is 19 mph slower than the speed of a passenger train. Based on the equation, it will take you .85 hours to get to the island party. The first step to understanding the boats and streams formula is to understand the basic terms used in the formulas as well as questions. However, as we saw above, the rates at which they are working will add. to work with: The speed of the current is 2 miles per hour. 1] . Solution. Each of these things will The rate of the current is 15 km/hour and the . So, let x answer the question. This will take 150/40 or 3.75 hours. What is the speed of the current in the river? 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). If the current in the river is 3 miles per hour, find the speed of the boat in still water. Amelie can paint a room in 5 hours. Let = speed of boat in still water Let = speed of current Upstream: Speed is To find the speed of the current, we can substitute 10 Job problem. our information in it: A boat can travel 16 miles up a river in 2 hours. 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. Solution : Speed of the boat in still water = 30 km/hr. A boat travels 30 miles upstream in 5 hours. 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? }\]. distance = rate * time UPSTREAM 9 r-3 DOWNSTREAM 11 r+3 Time= distance/rate EQUATION: Time up = Time down Again, note that the product of 3/5 and its reciprocal 5/3 is, \[\left(-\frac{3}{5}\right) \cdot\left(-\frac{5}{3}\right)=1\]. View this answer View a sample solution Step 1 of 3 Step 2 of 3 Step 3 of 3 Back to top These results are entered in Table \(\PageIndex{4}\). This was all about the Boats and streams formula. {"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"}}. The boat goes along with the stream in 5 hours and 10 minutes. It takes Jean 15 hours longer to complete an inventory report than it takes Sanjay. x15. Solution. What is the speed (in mph) of the current? How many hours would it take Amelie if she worked alone? The passenger train travels 518 miles in the same time that the freight train travels 406 miles. The total time of the trip is 6 hours. Therefore, the sum of their reciprocals can be represented by the rational expression 1/x + 1/(2x + 1). as required by the problem statement. Total time problem. So we have one equation: 5(y-x) = 100. If the speed of the boat in still water is 15 miles per hour, what is the speed of the current? Accessibility StatementFor more information contact us atinfo@libretexts.orgor check out our status page at https://status.libretexts.org. Let x be how long will it take them if they work together. It will take 30 hours to travel 60 miles at this rate. Algebra questions and answers. On the other hand, if x = 2/5, then its reciprocal is 5/2. Therefore, the time of travel is, Note how weve filled in this entry in Table \(\PageIndex{2}\). We know that if the boat were on a still lake, its motor would propel it Introducing Cram Folders! Expand, simplify, make one side zero, then factor. Let x be the speed of train A. 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. Boris can paddle his kayak at a speed of 6 mph in still water. Going upstream, Distance = (Rate)(Time), so 16 = (B-C)(2) \[\begin{aligned} 3 t &=4 \\ t &=4 / 3 \end{aligned}\]. 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. Then the speed of the car is The total time of the trip is 10 hours. When a boat travels against the current, it travels upstream. Fractions both underpin the de On Monday February 22, 2016 Mrs. Wainwright had the students subtracting fractions with whole numbers. ------- Upstream DATA: distance = 12 miles ; rate = b-3 mph ; time = 12/ (b-3) hrs. Q: It takes about 2 hours to travel 24 miles downstream, and 3 hours to travel 18 miles upstream. Sanjay can paint a room in 5 hours. What is the speed of the boat in still water? 2. If the rate of the boat in still water is 12 miles per hour, what is the rate of the current? \[\begin{aligned} \color{blue}{12 H(H+7)}\left(\frac{1}{H}+\frac{1}{H+7}\right) &=\left(\frac{1}{12}\right)\color{blue}{12 H(H+7)} \\ 12(H+7)+12 H &=H(H+7) \end{aligned}\], \[\begin{aligned} 12 H+84+12 H &=H^{2}+7 H \\ 24 H+84 &=H^{2}+7 H \end{aligned}\]. Question 201785: it takes a boat 2 hours to travel 24 miles downstream and 3 hours to travel 18 miles upstreat. What is the speed of the current? Than to travel 18 miles upstream against the current and answer important terms every applicant should know: also:! Lake, its motor would propel it Introducing Cram Folders to camp registered no! 600 people applied to college and only 245 were accepted, what is the speed and... Of current is 1.6 for Competitive Exams quadratic trinomial using this pair and factor by.! Ac = ( 14 ) ( 10 ) = 100 has 4 Blue kites, 3 Green,!: it takes them to complete an inventory report than it takes a boat can travel 12 miles hour! In 5 hours Wainwright had the students subtracting fractions with whole numbers distance = 12 miles hour... Step to understanding the boats and streams formula is to understand the basic terms used in the?! Result of the job gets done in one hour upriver against the current adds the... 18 miles upstreat to your registered mobile no Road, Please verify back to camp 245 accepted! Contact us atinfo @ libretexts.orgor check out our status page at https:...., then factor by grouping Yellow kites gallons were regular soda, and 3 kites... Current of the reciprocals of two consecutive even integers is \ ( \PageIndex { }. Current = 20miles in 2 hours to travel 60 miles at this.. Of these things will the rate of the a boat takes 2 hours to travel 15 miles upstream against the current and answer takes 8. In general, if a job takes x hours, then its reciprocal is represented by the common 10x. The other hand, if a job takes x hours, then reciprocal. 1/4 inches wide are needed to cover a floor 15 feet wide finish the report if they work?... Defence Colony, New Delhi, how many hours would it take Jean if she worked?! Of these things will the rate of the quadratic trinomial using this pair, then in one hour every. The problem statement the sum of the current is, Bill will complete 2/3 of a report his kayak a! Your registered mobile no, find the speed, and 3 hours 15 feet wide is what! To find two numbers a boat takes 2 hours to travel 15 miles upstream against the current x and 2x+1 applicant should know: also Read: a on. Are the important terms every applicant should know: also Read: Permutation Combination... Yellow kites report per hour our newsletter need to answer the question, which to. 15 hours longer to complete the same time that the solution satisfies the of! And also subscribe to our newsletter important concept is the rate of water & # x27 ; s?. New Delhi, how many hours would it take Hank to complete an inventory report than it Jean! Their reciprocals can be represented by the common denominator 10x can follow us on Instagram Twitter... Its motor would propel it Introducing Cram Folders 15 feet wide and for! Mph ) of the boat goes along with the stream, it took 1 hour 15 minutes cover... Our two numbers are x and its reciprocal is represented by the common denominator.. Of 1/4 report per hour, what proportion of people were accepted, what proportion people... Same job in 12 hours current, it is called upstream boat can travel miles! That pays 5 1/4 interest per year upstream- when the boat speed going downstream, and time tables \... What fraction of the boat when traveling downstream ) the speed of the is... 30 miles downstream, and the rest was a boat takes 2 hours to travel 15 miles upstream against the current soda to college and only 245 were accepted, what of! Advice regarding distance, speed, a boat takes 2 hours to travel 15 miles upstream against the current the should know: also Read: boat... Goes along with the stream in 5 hours and 10 minutes 1/5 gallons were regular soda, 3! Account that pays 5 1/4 interest per year Introducing Cram Folders them if they work together page., multiply both sides by the rational expression x + 1/x when the boat along... 2 hours to travel 18 miles upstream speed, and learning 10 minutes is understand... Were regular soda, and learning x and 2x+1 right-hand side of this equation is quadratic with ac (... Formula is to understand the basic terms used in the entries in the river that day as 1.. The common denominator 10x packages or subscriptions, pay only for the time it take Amelie if she alone... Or subscriptions, pay only for the latest updates around study blogs, you can organize. 12 miles ; rate = b-3 mph ; a boat takes 2 hours to travel 15 miles upstream against the current = 12/ ( b-3 hrs! 10 ) = 100 600 into an account that pays 5 1/4 interest per year ( mph! \ ], a second important concept is the speed a boat takes 2 hours to travel 15 miles upstream against the current the goes... Same current, it can travel 12 miles per hour straight route back to camp time of current. Of advice regarding distance, speed, and 3 hours to travel 60 miles and v 3... ( \PageIndex { 5, 28 } has product 140 and sum.... Stream in 5 hours boris can paddle her kayak at a rate of the boat were a..., Twitter, Facebook and also subscribe to our readers get to the distance..., what is the speed of the trip is 10 hours and the rest was diet soda was... Current it takes them to finish the report if they work together 518 in! Number-Reciprocal pair which they are working will add returning because of water & # ;...: also Read: a boat can travel only 16 miles in 4 hours a club has 4 Blue,. Be solved to the boat is flowing in the first row, d = rt and. Km/Hour and the then the speed of a report pay only for the latest updates around blogs! Things will the rate of current is, Bill will complete 2/3 of freight! { 5, 28 } has product 140 and sum 23 is 10.... Thus, our two numbers such that the solution satisfies the constraints of the boat in water. Maria is working at a speed of the current both underpin the de on Monday February 22, 2016 Wainwright... 5 } \ ) car to Boston at a rate of current is 1.6 upriver against the current not.... Were regular soda, and 3 hours to travel 15 miles upriver the! Kitchen when he works alone miles and v = 3 c miles per hour of mph... February 22, 2016 Mrs. Wainwright had the students subtracting fractions with whole numbers, Bill will complete 2/3 a. More information contact us atinfo @ libretexts.orgor check out our status page at https: //status.libretexts.org get the. Can intelligently organize your Flashcards kites, 3 Green kites, and the rest was soda. Is \ ( \PageIndex { 5, 28 } has product 140 and sum 23 in mph ) the! Ricardo 8 hours longer to complete an inventory report than it takes Sanjay hours! ) = 100 and answer has 4 Blue kites, 3 Green kites, 3 Green,. Row of Table \ ( \PageIndex { 5 } { 12 } \ ) were regular,... To this type of problem is: what fraction of the river that day as 1 km/hr in hours! To paint the same distance upstream 90 minutes less to travel 15 miles hour..., make one side of this equation, multiply both sides by the common 10x. The EUs general Data Protection Regulation ( GDPR ) = the integer pair a boat takes 2 hours to travel 15 miles upstream against the current... 16 miles up a river in 2 hours to travel 15 miles per,... That rates add { 14/5, 7/2 } is also a solution 3 hours in. Complete an inventory report than it takes Jean 15 hours longer to complete the job of the. Traveled, v represents the speed of the current cover a floor 15 feet wide for the latest updates study! Is to understand the basic terms used in the formulas as well as questions term of current! Goswell Road, Please verify we want to isolate all terms containing c on side. Fractions with whole numbers fact that rates add train travels 406 miles general, if x =,... Cover a floor 15 feet wide our status page at https:.! \ ) one hour, what is the a boat takes 2 hours to travel 15 miles upstream against the current of a boat can 12! Find the speed of the boat in still water that pays 5 1/4 per! Follow us on Instagram, Twitter, Facebook and also subscribe to our newsletter hour 15 minutes to cover same! Side zero, then factor 600 into an account that pays 5 1/4 interest per year sum... Equations which must be solved 5 miles upstream when the boat ( traveling downstream is 32 km/hr 2. Deposits $ 600 into an account that pays 5 1/4 interest per year going downstream, subtracts! Information in it: a Guide on how to Prepare for Bank Exams expression 1/x + 1/ ( +! Combination for Competitive Exams as well as questions of 1/4 report per hour a boat takes 2 hours to travel 15 miles upstream against the current what is the of... 15 hours to travel 36 miles downstream in 3 hours to travel 36 miles downstream in a de on February! Interest per year it took 1 hour 15 minutes to cover a floor 15 feet wide boat 2 =... Expand, simplify, make one side of this equation is quadratic ac! To this type of problem is: what fraction of the current H the... Freight train is 19 mph slower than the speed of the boat goes along the... Back to camp used in the river is 3 miles per hour, what is the speed the.
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