A sink can be filled by the cold water faucet in 6 minutes. The drain can empty a full sink in 8 minutes. If the sink is empty and both the cold water faucet and the drain are open, how long will it take the sink to overflow?
A)27 minutes
B)21 minutes
C)24 minutes
D)25 minutes
E)26 minutes

Question

Quizplus · Accepted Answer

Let's denote the amount of water that fills the sink in one minute as "x", and the amount of water that drains out of the sink in one minute as "y".
We know that:
x = 1/6 (since it takes 6 minutes to fill the sink)
y = 1/8 (since it takes 8 minutes to empty the sink)
When both the faucet and the drain are open, the net amount of water that enters the sink each minute is:
x - y = 1/6 - 1/8 = 1/24
Therefore, the amount of time it takes the sink to overflow is:
1 / (x - y) = 1 / (1/24) = 24 minutes

So, the best choice is C) 24 minutes.

A Sink Can Be Filled by the Cold Water Faucet