SOLUTION: Two pumps of different sizes working together can empty a tank in 3 hours. The larger pump can empty this tank in 5 hours. How long will it take the smaller one to do the job alone

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Question 393202: Two pumps of different sizes working together can empty a tank in 3 hours. The larger pump can empty this tank in 5 hours. How long will it take the smaller one to do the job alone? Show the 4-step process.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Two pumps of different sizes working together can empty a tank in 3 hours.
The larger pump can empty this tank in 5 hours.
How long will it take the smaller one to do the job alone?
:
Let t = time required by the small pump alone
:
Let the completed job = 1 (an empty tank)
:
Each pump will do a fraction of the job, the two fractions add up to 1
:
3%2F5 + 3%2Ft = 1
Multiply by 5t, results
3t + 5(3) = 5t
:
15 = 5t - 3t
15 = 2t
t = 15%2F2
t = 7.5 hrs, the small pump alone
;
:
Check the solution
3%2F5 + 3%2F7.5 =
.6 + .4 = 1; confirms our solution