SOLUTION: An inlet pipe can fill a pool in 3 hours. The outlet pipe takes 12 hours to empty the pool. How long will it take to fill the pool if both pipes are open?

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Question 721106: An inlet pipe can fill a pool in 3 hours. The outlet pipe takes 12 hours to empty the pool. How long will it take to fill the pool if both pipes are open?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The work at opposite signs, but their rates still can combine through addition.

Use rates in the form of jobs per unit time.
Inlet pipe rate is +1/3 pools per hour.
Outlet pipe rate is -1/12 pools per hour.

Both pipes operating at the same time is of rate 1%2F3%2B%28-1%2F12%29=1%2F3-1%2F12 pools per hour. Rate is positive 3%2F12=1%2F4 pools per hour. This is simply 4 hours to fill the pool.