A tap fills a water drum in 10 hours, but a crack at the bottom would empty the full drum in 30 hours. With the tap on and the crack leaking, how long does the empty drum take to fill?

15 hoursCorrect answerYour answer20 hoursCorrect answerYour answer30 hoursCorrect answerYour answer40 hoursCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

Net rate = $\frac{1}{10} - \frac{1}{30} = \frac{3-1}{30} = \frac{1}{15}$ per hour.
So the drum fills in 15 hours.

Worth noting

A leak works against the tap, so subtract its rate. Subtracting the hours $(30 - 10)$ gives 20 hours, and 40 hours adds them.

Ten questions from Time & Work, at your own pace.

Explanation