Multiple choice

Two pipes A and B can fill a cistern in $\displaystyle 37\frac{1}{2}$ min and $45$ min respectively. Both pipes were opened and the cistern was filled in just $\displaystyle \frac{1}{2}$ an hour if the pipe B is turned off after what time it is opened?

  1. $5$ min
  2. $9$ min
  3. $10$ min
  4. $15$ min
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A fills 1/37.5 = 2/75 per min. B fills 1/45 per min. If B is turned off after t minutes, A works for 30 mins. (2/75)*30 + (1/45)*t = 1. 4/5 + t/45 = 1. t/45 = 1/5. t = 9 minutes.

AI explanation

Pipe A fills 2/75 of the cistern per minute and pipe B fills 1/45 per minute. If pipe B is turned off after x minutes, the total work done is x(1/45) + 30(2/75) = 1. This simplifies to x/45 + 60/75 = 1, so x/45 + 4/5 = 1, which gives x/45 = 1/5 and x = 9. Pipe B is turned off after 9 minutes.

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