SOLUTION: Two pipes can be used to fill a pool. Working together the two pipes can fill the pool in 4 hours. The larger pipe can fill the pool in 4 hours less time than the smaller pipe ca

Question 112965: Two pipes can be used to fill a pool. Working together the two pipes can fill the pool in 4 hours. The larger pipe can fill the pool in 4 hours less time than the 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 ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Two pipes can be used to fill a pool. Working together the two pipes can fill the pool in 4 hours. The larger pipe can fill the pool in 4 hours less time than the 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.
:
Let t = time required for the smaller pipe to fill the pool alone
then
(t-4) = time required for the larger pipe
:
Let the filled pool = 1
:
+ = 1
:
Multiply equation by t(t-4) to get rid of the denominators:
t(t-4)* + t(t-4)* = t(t-4)*1
:
Cancel out the denominators and you have:
4(t-4) + 4t = t(t-4)
:
4t - 16 + 4t = t^2 - 4t
:
8t - 16 = t^2 - 4t
:
Arrange as a quadratic equation:
0 = t^2 - 4t - 8t + 16
:
t^2 - 12t + 16 = 0
:
WE have to solve this using the quadratic equation: a=1; b=-12; c=16
:

t = 1.528, obviously this is not the solutions
:
Solution 2:

:
t = 10.472 ~ 10.5 hrs required by the small pipe to fill the pool
:
:
Check solution:
4/10.5 + 4/6.5 =
.4 + .6 = 1

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