Help with a flow rate problem!

Question

A water tank can be filled in 6 minutes and emptied in 8 minutes. if the drain is accidentally left open when the tank is being filled, how long does it take to fill the tank? 

Answer 1

The rate of filling is 1/6 of the tank per minute, because if this rate per minute were multiplied by 6 minutes, the product (result) is 1, meaning 100% full. Similarly the rate of loss is 1/8 of tank per minute.

 

The net rate of filling is 1/6 - 1/8. This equals (8-2) / 72 = 6 / 72 = 1/12 of full tank per minute.  So it will fill up in 12 minutes.