Variation on Combined Work
Date: 06/13/2002 at 01:45:33 From: Vibhuti Dhand Subject: word problems in linear equations in two variables It takes 12 hours to fill a swimming pool using two pipes. If the larger pipe is used for 4 hours and the smaller for 9 hours, only half of the pool is filled. How long would it take for each pipe alone to fill the pool?
Date: 06/13/2002 at 13:18:07 From: Doctor Ian Subject: Re: word problems in linear equations in two variables Hi Vibhuti, It sounds to me like you're saying: A large pipe can fill 1/2 a pool in 4 hours. A small pipe can fill 1/2 the same pool in 9 hours. Together, the pipes can fill the pool in 12 hours. But this can't be right, because then the answers are trivial: The large pipe can fill the pool in 8 hours, and the small one can fill it in 18. Or are you saying: If you run a large pipe for 4 hours, and run a small pipe for 9 hours, you can fill 1/2 a pool. If you run both pipes together for 12 hours, you can fill the whole pool. Is that correct? If so, let's say that the pool holds G gallons, that the large pipe contributes R gallons per hour, and the small pipe contributes r gallons per hour. Then 4R + 9r = G/2 (First condition) 12(R + r) = G (Second condition) Doubling the first equation gives us 8R + 18r = G 12(R + r) = G Two things that are equal to the same thing are equal to each other, so 8R + 18r = 12(R + r) So you can use this to find out the ratio of the rates for the two pipes, R = kr Then you can substitute that back into the equation 12(kr + r) = G to find out how long the smaller pipe needs to fill the whole pool; which will tell you how long it takes the larger pipe to fill the whole pool. Can you take it from here? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/
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