Question

A winery has a vat with two pipes leading to it. The inlet pipe can fill the vat in 3 hours, while the outlet pipe can empty it in 7 hours. How long will it take to fill the vat if both pipes are left open

Answer 1

5 1/4 hours

Explanation:

The rate of filling is 1/3 vats per hour. The rate of emptying is 1/7 vats per hour, so the net rate of filling is ...

(1/3) -(1/7) = 4/21 . . . . vats per hour

Then for filling one vat, it will take an amount of time that is the inverse of this:

21/4 = 5 1/4 . . . hours per vat

If both pipes are left open, the vat will fill in 5 1/4 hours.