winery math question

Question

A winery has a 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 110 hours. How long will it take to fill the vat if both pipes are left? open?

Answer 1

t represents the time

 

In t hours the inlet fills t/7

In t hours the outlet drains -t/110

 

Together the fill the one tank.

 

t/7 - t/110 = 1          multiply both sides by the LCM, 770

110t - 7t = 770

103t = 770

t ≈ 7.47572816

 

The tank fills in slightly less than seven and one-half  hours.