SOLUTION: Pipe A can fill a tank in 7 hours more than pipe B can. If A is opened for as many hours as it would take B to fill a tank, B can complete the filling 5 hours. How long does it tak

Question 778933: Pipe A can fill a tank in 7 hours more than pipe B can. If A is opened for as many hours as it would take B to fill a tank, B can complete the filling 5 hours. How long does it take each pipe, alone, to fill a tank?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Pipe A can fill a tank in 7 hours more than pipe B can.
If A is opened for as many hours as it would take B to fill a tank, B can complete the filling 5 hours.
How long does it take each pipe, alone, to fill a tank?
:
Let t = time required by pipe B alone
then
(t+7) = time required by pipe A
:
Let the completed job = 1; (a full tank)
:
A shared work equation, each pipe does a fraction of the job
The two fractions add up to 1
:
+ = 1
multiply equation by t(t+7), to clear the denominators, resulting in:
t^2 + 5(t+7) = t(t+7)
t^2 + 5t + 35 = t^2 + 7t
Subtract t^2 from both sides
5t + 35 = 7t
35 = 7t - 5t
35 = 2t
t = 35/2
t = 17.5 hrs for B to fill the tank alone
then
17.5 + 7 = 24.5 hrs for A to do it
:
:
Check this with a calc
+ = 1
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