A winery vat with two pipes leading to it. The inlet pipe can fill the vat in 7 hours, while the outlet pipe can empty it in 9 hours. How long will it take to fill the vat if both pipes are left open?

Solution:

The time is t

So

1/7 +1/9 = 1/t

t = 63/16

So it takes 63/16 hours to fill the vat if both pipes are left open