A bathtub can be filled by the cold water faucet in 17 minutes and by the hot water faucet in 18 minutes. The drain can empty the tub in 14 minutes. Can the tub be filled if both faucets and the drain are open?
A) No
B) Yes

Question

Quizplus · Accepted Answer

The rate at which the cold water faucet fills the tub is 1/17 of the tub per minute. The rate at which the hot water faucet fills the tub is 1/18 of the tub per minute. The rate at which the drain empties the tub is 1/14 of the tub per minute. 
Therefore, the combined rate of both faucets filling the tub is 1/17 + 1/18 = 35/306 of the tub per minute. 
At the same time, the drain is emptying the tub at a rate of 1/14 of the tub per minute. 
To determine if the tub can be filled, we need to compare the combined rate of the faucets filling the tub to the rate at which the drain is emptying the tub. 
35/306 is greater than 1/14, so the tub can be filled if both faucets and the drain are open.

A Bathtub Can Be Filled by the Cold Water Faucet