Filling a vat in a winery

Question

A winery has a vat with two pipes leading to it. The inlet pipe can fill the vat in 4 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?

Answer 1

Let's figure out how much each pipe affects the amount of wind in the vat per hour.

 

The inlet pipe fills the vat in 4 hours, which means that it increases the amount of wine in the vat at a rate of 1/4 of the vat per hour.

 

Similarly, the outlet pipe decreases the amount of wine in the vat at a rate of 1/9 of the vat per hour.

 

So the net effect of the two pipe is to increase the amount of wine at a rate of 1/4 - 1/9 of the vat per hour. 

 

1/4 - 1/9 = 9/36 - 4/36 = 5/36

 

So with both pipes open, the vat will fill at a rate of 5/36 of the vat in one hour.  That means that the entire vat will fill up in 1 / (5/36) hour = 36/5 = 7.2 hours.