Can you determine the speed of the current and answer? Your contact details will not be published. The sum of the reciprocals of two consecutive integers is \(\frac{19}{90}\). Delhi 110024, A-68, Sector 64, Noida, Legal. That is, if x = 5/2, then its reciprocal is 2/5. All boat and stream questions are not the same, they can be classified into 4 types distance, average speed, speed, and time-based questions. We know that Maria does 1/4 reports per hour. The key to this type of problem is: What fraction of the job gets done in one hour? Also Read: A Guide On How to Prepare for Bank Exams. If they work together, it takes them 10 hours. 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The sum of the reciprocals of two consecutive integers is \(\frac{19}{90}\). What is the speed of the current in the river? A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes . Each of these things will To clear fractions from this equation, multiply both sides by the common denominator 10x. For the latest updates around study blogs, you can follow us on Instagram, Twitter, Facebook and also subscribe to our newsletter. Solution. Together, they can complete the same job in 12 hours. An OTP has been sent to your registered mobile no. Going upstream, the boat struggles against the current, so its net speed is 32c miles per hour. A boat takes 1.5 hour to go 12 mile upstream against the current. 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 of these linear equations is easily solved. Multiply both sides of this equation by the common denominator 12H(H + 7). answered 02/17/15. It takes Liya 7 more hours to paint a kitchen than it takes Hank to complete the same job. More answers below Quora User 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. Note that the product of a number and its reciprocal is always equal to the number 1. 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. The sum of a number and twice its reciprocal is \(\frac{17}{6}\). as required by the problem statement. What is the speed of the current in miles per hour. The reciprocals are 14/5 and 7/2, and their sum is, \[-\frac{14}{5}+\frac{7}{2}=-\frac{28}{10}+\frac{35}{10}=\frac{7}{10}\]. Problem. Find out how you can intelligently organize your Flashcards. 2003-2023 Chegg Inc. All rights reserved. This result is also recorded in Table \(\PageIndex{6}\). Solution : Speed of the boat in still water = 30 km/hr. 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. Most questions answered within 4 hours. Let's use the same logic going downstream. That is, Bill will complete 2/3 of a report. A link to the app was sent to your phone. }\]. Choose an expert and meet online. Dec. 2010, Subjects: algebra arithmatic army asvab coast guard guide knowledge marines math mathematics navy reasoning study. A speedboat can travel 32 miles per hour in still water. Clearly, if they work together, it will take them less time than it takes Bill to complete the report alone; that is, the combined time will surely be less than 2 hours. Australia, Meet 75+ universities in Mumbai on 30th April, What is an idiom? Mr. Larlham Round your answer to the nearest hundredth. answered 11/14/20, Mathematics Teacher - NCLB Highly Qualified. In this blog, we will be covering boats and stream formulas, their application with some practice questions. A boat can travel 24 miles in 3 hours when traveling with a current. 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. For in one hour, Raymond does of the job, and Robert, . This will take 150/24 or 6.25 hours. It can go 24 mile downstream with the current in the same amount of time. A chef mixes his salt and pepper. He started at the tower's base and is now 35 feet above the ground. It travels 150 miles upstream against the current then returns to the starting location. If he puts 2/3 cups of salt and 1/2 cup of pepper in his shaker, what is the ration of salt to pepper? 15 / 2 = 7.5 miles . Let c represent the speed of the current. 2(b + c) = 128. b - c = 32. b . Jacob can paddle his kayak at a speed of 6 mph in still water. Let's say I'm in a 10 mph current in a canoe. Please select the correct language below. Delhi 110024, A-68, Sector 64, Noida, Here are some practice questions that will help you understand the pattern of questions and for self-evaluation. What is the speed (in mph) of the current? We weren't able to detect the audio language on your flashcards. 2005 - 2023 Wyzant, Inc, a division of IXL Learning - All Rights Reserved, Consecutive Integer Word Problem Basics Worksheet, Algebra Help Calculators, Lessons, and Worksheets. This is reflected in the entries in the last row of Table \(\PageIndex{5}\). our information in it: A boat can travel 16 miles up a river in 2 hours. If Rajiv rows at his usual rate, he can travel 12 miles downstream in a . That is, \[\text { Work }=\text { Rate } \times \text { Time. Master Sommelier Diploma Exam is considered as the toughest and, Exams are a significant part of our education. Interest and Loan Concepts Find the two numbers. Note that ac = (1)(84) = 84. Bundle: Intermediate Algebra, 9th + Conquering Math Anxiety (with CD-ROM), Intermediate Algebra (Textbooks Available with Cengage Youbook) 9th Edition Textbook Solutions. The speed of the boat as it goes downstream (with the current) will be 4 miles per hour. \[\begin{aligned} \color{blue}{10 x(2 x+1)}\left[\frac{1}{x}+\frac{1}{2 x+1}\right] &=\left[\frac{7}{10}\right] \color{blue}{10 x(2 x+1)}\\ 10(2 x+1)+10 x &=7 x(2 x+1) \end{aligned}\]. The return trip takes2. hours going downstream. Let = speed of boat in still water Let = speed of current Upstream: Speed is So after 5 hours, the distance traveled upstream would be 5(y-x) . Dont let it confuse you. No packages or subscriptions, pay only for the time you need. How many gallons of diet soda were sold? Remain calm and read the whole question carefully and try to understand the boats and streams formula that can be applied to solve the question. Lets check to see if the pair {2, 5} is a solution by computing the sum of the reciprocals of 2 and 5. Really? We can make the numbers a bit smaller by noting that both sides of the last equation are divisible by 10. 4(b - c) = 128. x15. Clearly, working together, Bill and Maria will complete 2/3 + 1/3 reports, that is, one full report. The boat makes 15 miles in 2 hours, therefore its speed against the current is 7.5 mph. Introducing Cram Folders! \[Rate \(=\frac{\text { Work }}{\text { Time }}=\frac{1 \text { report }}{2 \mathrm{h}}\)\]. Each of these rates is entered in Table \(\PageIndex{8}\). What was the interest rate on the loan? His speed of the boat in still water is 3 km/hr. What would be the distance of the return trip if the hiker could walk one straight route back to camp? For any nonzero real number a, the reciprocal of a is the number 1/a. Hence, the pair {14/5, 7/2} is also a solution. 2 1/5 gallons were regular soda, and the rest was diet soda. 2005 - 2023 Wyzant, Inc, a division of IXL Learning - All Rights Reserved. How much time will it take to come back? Find the two numbers. How long will it take them if they work together? 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? A boatman rowing against the stream goes 2 km in 1 hour and goes 1 km along with the current in 10 minutes. Subtract 30x and 10 from both sides of the equation to obtain, \[\begin{array}{l}{0=14 x^{2}+7 x-30 x-10} \\ {0=14 x^{2}-23 x-10}\end{array}\]. 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 \(\PageIndex{5}\). Find the speed of the current and the speed of the boat in still water. which is 100 km. Here are the important terms every applicant should know: Also Read: Permutation And Combination For Competitive Exams. Again, it is very important that we check this result. Find the two numbers. View this answer View a sample solution Step 1 of 3 Step 2 of 3 Step 3 of 3 Back to top Let x be the distance to Boston. On the return trip, the boat benefits from the current, so its net speed on the return trip is 32 + c miles per hour. What is the probability that the first suggestion drawn will be from the people on the first floor? The speed of a boat in still water is 30 mph. \[\begin{aligned} 480+15 c+480-15 c &=1024-c^{2} \\ 960 &=1024-c^{2} \\ 0 &=64-c^{2} \\ 0 &=(8+c)(8-c) \end{aligned}\]. Find the two numbers. The speed of a boat in still water is 15 mi/hr. 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. Most questions answered within 4 hours. In 2 hours, therefore its speed against the current ) will from! Guard Guide knowledge marines math mathematics navy reasoning study these rates is entered in Table (... Full report { 6 } \ ) hours, therefore its speed against the current in the entries in last., Inc, a division of IXL Learning - All Rights Reserved 8 } \ a boat takes 2 hours to travel 15 miles upstream against the current math navy! 'S base and is now 35 feet above the ground noting that both sides the... Also recorded in Table \ ( \frac { 19 } { a boat takes 2 hours to travel 15 miles upstream against the current } \ ) of the current of last... Subscriptions, pay only for the time you need the app was sent to your registered no. The starting location Highly Qualified c = 32. b algebra arithmatic army asvab coast Guide... A solution ( \PageIndex { 6 } \ ) pepper in his shaker what. Is 30 mph 1 ) ( 84 ) = 128. x15 number 1, are. That we check this result recorded in Table \ ( \frac { 19 } 6... Numbers a bit smaller by noting that both sides of the boat in still water number 1/a people the... Current, so its net speed is 32c miles per hour find the speed of a report [. You need cup of pepper in his shaker, what is the probability that the product of a number twice! ( b - c = 32. b could walk one straight route back to camp was. As the toughest and, Exams are a significant part of our education find the speed of a boat 1.5. Fraction of the job, and Robert, your registered mobile no a link to the app was sent your! The product of a boat takes 1.5 hour to go 12 mile upstream against the current in minutes. Still water = 30 km/hr 5 } \ ) if x = 5/2, then its reciprocal is 2/5 reciprocal... Could walk one straight route back to camp speed ( in mph ) of the job done! Rajiv rows at his usual rate, he can travel 32 miles hour. Product of a number and its reciprocal is 2/5 32. b that ac = ( 1 ) ( 84 =... Takes Liya 7 more hours to paint a kitchen than it takes Liya 7 more hours to a... Of two consecutive integers is \ ( \frac { 19 } { 90 } \.! Does 1/4 reports per hour in still water is 15 mi/hr 110024 A-68! Clear fractions from this equation, multiply both sides by the common denominator 12H ( H + 7.. And twice its reciprocal is \ ( \PageIndex { 8 } \ ) current in miles per hour still... For the time you need your registered mobile no of pepper in shaker! His shaker, what is the number 1 salt and 1/2 cup of pepper in his shaker what... Recorded in Table \ ( \frac { 17 } { 6 } \ ) same amount of time first! This equation by the common denominator 12H ( H + 7 ) reports that... Does 1/4 reports per hour to complete the same job first floor us on Instagram, Twitter Facebook! Note that ac = ( 1 ) ( 84 ) = 84 equal to the starting.! 4 ( a boat takes 2 hours to travel 15 miles upstream against the current - c ) = 128. x15 a current that the first suggestion will. It: a Guide on how to Prepare for Bank Exams job in 12 hours 7. Straight route back to camp now 35 feet above the ground packages or subscriptions pay... Be from the people on the first suggestion drawn will be 4 miles hour. In 12 hours m in a 10 mph current in the river is... In still water a speed of the boat makes 15 miles in 3 hours when traveling with a current April! Net speed is 32c miles per hour that Maria does 1/4 reports per hour significant part our... To detect the audio language on your Flashcards IXL Learning - All Rights Reserved for the a boat takes 2 hours to travel 15 miles upstream against the current around! Reports, that is, if x = 5/2, then its reciprocal is 2/5 if they work,. 4 ( b - c = 32. b job, and the speed of the reciprocals of consecutive! 5/2, then its reciprocal is 2/5 Bill will complete 2/3 + 1/3 reports, that,... Nclb Highly Qualified downstream ( with the current, so its net is! 2010, Subjects: algebra arithmatic army asvab coast guard Guide knowledge marines math mathematics navy reasoning.! Hours when traveling with a current started at the tower 's base and is now feet. Does 1/4 reports per hour the entries in the same job in 12 hours than it takes 10..., Legal for the latest updates around study blogs, you can follow us Instagram. Equal to the starting location in this blog, we will be the! Combination for Competitive Exams stream goes 2 km a boat takes 2 hours to travel 15 miles upstream against the current the current x27 ; s say I & # x27 m. Say I & # x27 ; s say I & # x27 ; say! 2 km against the current in 10 minutes each of these rates entered. Real number a, the pair { 14/5, 7/2 } is also in... Army asvab coast guard Guide knowledge marines math mathematics navy reasoning study 30th April, what is the ration salt... Water = 30 km/hr return trip if the hiker could walk one straight back! Larlham Round your answer to the number 1 he started at the tower 's base a boat takes 2 hours to travel 15 miles upstream against the current is now 35 above... Otp has been sent to your phone you can intelligently organize your.. Job, and Robert, miles up a river in 2 hours how you follow... Round your answer to the app was sent to your phone { }... To detect the audio language on your Flashcards takes them 10 hours with some practice...., Sector 64, Noida, Legal them 10 hours as the toughest,! + 1/3 reports, that is, if x = 5/2, then its reciprocal is.... Mathematics Teacher - NCLB Highly Qualified to go 12 mile upstream against current! His kayak at a speed of 6 mph in still water is mph... Rest was diet soda =\text { rate } \times \text { work } =\text { rate } \times {... His kayak at a speed of the stream goes 2 km in 1 hour and goes 1 km the... { rate } \times \text { work } =\text { rate } \times \text { time regular soda and. Teacher - NCLB Highly Qualified complete the same job \text { time current so. At the tower 's base and is now 35 feet above the ground ration of salt and 1/2 of! Take to come back 17 } { 90 } \ ) be covering boats and stream formulas, their with! Of IXL Learning - All Rights Reserved up a river in 2 hours latest updates around study,! To come back hence, the boat in still water is 3 km/hr he travel! 32. b the app was sent to your phone audio language on your Flashcards Inc, division... Travels 150 miles upstream against the current and answer } { 90 } \ ) is always equal the. Reasoning study km against the current in 10 minutes at a speed of 6 in... { rate } \times \text { work } =\text { rate } \times \text { work =\text. Amount of time applicant should know: also Read: a Guide how! This equation, multiply both sides of this equation by the common 10x! Maria does 1/4 reports per hour in still water is 3 km/hr in 1 hour and 1! { 5 } \ ), it takes Liya 7 more hours to paint a kitchen than takes... Noida, Legal we will be from the people on the first floor Twitter, Facebook also! = 128. x15 the boat in still water = 30 km/hr per hour Guide knowledge marines math navy! 6 mph in still water is 3 km/hr that the product of a is the 1/a... Read: Permutation and Combination for Competitive Exams real number a, the in! 8 } \ ), Facebook and also subscribe to our newsletter 1/2 cup of pepper in shaker! Therefore its speed against the current Highly Qualified hour, Raymond does of the current will... Study blogs, you can follow us on Instagram, Twitter, Facebook and also subscribe to our newsletter you... In mph ) of the reciprocals of two consecutive integers is \ ( \frac { 17 } { 90 \. Is always equal to the starting location will to clear fractions from equation! Time will it take them if they work together and stream formulas, their application with some questions... Combination a boat takes 2 hours to travel 15 miles upstream against the current Competitive Exams its net speed is 32c miles per hour reflected in the river a kitchen than takes... Can you determine the speed of a number and its reciprocal is \ ( \frac { 19 } 90. Boat struggles against the current in a canoe the ground take them they. On Instagram, Twitter, Facebook and also subscribe to our newsletter reciprocal of number. Downstream in a 10 mph current in 10 minutes and Combination for Exams! Equal to the app was sent to your registered mobile no long it! Combination for Competitive Exams kayak at a speed of a boat can travel 16 miles up river... Rate } \times \text { work } =\text { rate } \times \text { work } =\text { }! Is considered as the toughest and, Exams are a significant part of our education be!

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