Filling a PoolDate: 07/28/97 at 21:28:15 From: moms address) (Jennifer Mann Subject: Word Problem - fractions? It takes 2 hours to fill a pool with the green hose, but 5 hours with the black hose - how long does it take to fill it with both hoses at same time ? My solution: after one hour the green hose fills 1/2 of the pool and the black hose fills 1/5 of the pool. After 1 hour the pool is 1/2 + 1/5 full, or 7/10 full. How much longer would it be for the remaining 3/10 ? I come up with 3/7 of an hour or 3/7(60 minutes) or 25 minutes with 5/7 minute. My answer does not quite make sense to me (or my mom). One hour 25 minutes and 5/7 of a minute ?! Date: 07/29/97 at 07:42:39 From: Doctor Anthony Subject: Re: Word Problem - fractions ? You are thinking along the right lines. In 1 hour, with both hoses, you fill 1/2 + 1/5 = 7/10 of the pool. So to fill the pool you require 10/7 = 1 hour 25 mins 42.86 seconds Note that to get the total time, you simply find the reciprocal of 7/10. It is not necessary to consider the remaining 3/10 in the way you did, although you will of course get the right answer, but only after a few extra steps. To understand why 10/7 gives the total time, consider an easier situation. Suppose we fill 1/3 of the pool in 1 hour: then it is obvious that it will require 3 hours to fill the pool. Or suppose we fill 1/2 of the pool in 1 hour: then it would take 2 hours to fill the pool. In each case the total time in hours is the reciprocal of the fraction filled in 1 hour. In arithmetic notation, fraction per hour x number of hours = 1 number of hours = 1/fraction per hour -Doctor Anthony, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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