SOLUTION: Two Pipes can be used to fill a pool. Working together the two pipes can fill the pool in four hours. The larger pipe can fill the pool in four hours less time that then smaller

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Question 112967: Two Pipes can be used to fill a pool. Working together the two pipes can fill the pool in four hours. The larger pipe can fill the pool in four hours less time that then smaller pipe can alone. Find the time to the nearest tenth of an hour it takes for the smaller pipe working alone to fill the pool.
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!

Let t=time it takes the smaller pipe to fill the pool
Then the smaller pipe fills at the rate of 1/t pools per hour
t-4 =time it takes the larger pipe to fill the pool
The larger pipe fills at the rate of 1/(t-4) pools per hour
Working together, the two pipes fill the pool at the rate of 1/4 pool per hour so our equation to solve is:
(1/t)+1/(t-4)=1/4 multiply each term by 4t(t-4)
4(t-4)+4t=t(t-4) get rid of parens (distributive law)
4t-16+4t=t^2-4t subtract t^2 from and add 4t to both sides
4t-16+4t+4t-t^2=t^2-t^2-4t+4t collect like terms
12t-16-t^2=0 multiply each term by -1 and rearrange
t^2-12t+16=0---------------------quadratic in standard form--- solve using the quadratic formula:
t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
t+=+%2812+%2B-+sqrt%28+%28-12%29%5E2-4%2A1%2A16+%29%29%2F%282%2A1%29+
t+=+%2812+%2B-+sqrt%28+%28144-64%29%29%29%2F%282%29+
t+=+%2812+%2B-+sqrt%28+%2880+%29%29%29%2F%282%29+
t+=+%2812+%2B-+8.944+%29%2F%282%29+
t+=+%2812+%2B8.944+%29%2F%282%29+
t=10.472 or 10.5 hours--------------------------------answer
and
t+=+%2812+-+8.944+%29%2F%282%29+
t=1.528 or 1.5 hours ---(Note:This cannot be a correct answer. It would require the larger tank to fill in (1.5-4) which would yield negative hours)
CK
1/10.5+1/6.5=1/4
(10.5+6.5)/68.25=1/4
17/68.5=1/4
~~~1/4=1/4
Hope this helps---ptaylor