SOLUTION: It takes 30 minutes to empty a half-full tank by draining it at a constant rate. It is decided to simultaneously pump water into the half-full tank while draining it. What is the

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Question 873563: It takes 30 minutes to empty a half-full tank by draining it at a constant rate. It is decided to
simultaneously pump water into the half-full tank while draining it. What is the rate at which
water has to be pumped in so that it gets fully filled in 10 minutes?
Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
The objective is to fill (1/2) tank. The rate of the emptying pipe and the filling pipe is the sum of them. The unknown rate for the filling pipe is a positive 1/x, and x is some unknown minutes.

Pipe for emptying, -%281%2F60%29 tank per minute.
Pipe for filling, 1%2Fx tank per minute.
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highlight%28%281%2Fx-1%2F60%29%2A10=1%29, which is R*t=v, using v as the whole tank volume. The actual volume measure is the tank unit, no matter as gallons or liters, or whatever specific volume measure.

%2860-x%2910=60x
60-x=6x
60=5x
highlight%28x=12%29, meaning the fill pipe must be used at a rate of 12 minutes to fill the tank if it were working alone.