Pipe A fills a tank in 12 minutes and pipe B in 20 minutes. They are opened one at a time for a minute each, in turn, starting with A. How long does the empty tank take to fill?

14\frac{4}{5}

minutesCorrect answerYour answer

7\frac{1}{2}

minutesCorrect answerYour answer15 minutesCorrect answerYour answer

15\frac{1}{5}

minutesCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

Each 2-minute cycle fills $\frac{1}{12} + \frac{1}{20} = \frac{5+3}{60} = \frac{8}{60}$ .
7 cycles (14 minutes) fill $\frac{56}{60}$ , leaving $\frac{4}{60}$ .
Minute 15 is A's, and A fills $\frac{5}{60}$ per minute, so it needs $\frac{4}{5}$ of that minute.
Total = $14\frac{4}{5}$ minutes.

Worth noting

Doubling the together time ( $7\frac{1}{2} \times 2 = 15$ minutes) ignores that the tank fills before the 8th cycle ends. Starting with B instead would give a different answer, so read who goes first.

Concept: Pipes opened alternately
Typical timeTypical: 120 s
Your timeYours: —

The rule this testsPipes and cisterns

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

Pipe A fills a tank in 12 minutes and pipe B in 20 minutes. They are opened one at a time for a minute each, in turn, starting with A. How long does the empty tank take to fill?

Explanation