Multiple choice

Two taps A and B can fill a cistern in 371/2 minutes and 45 minutes, respectively. Both taps are turned on. When must the second tap be turned off, so that the cistern is filled in half an hour?

  1. After 7 minutes

  2. After 9 minutes

  3. After 12 minutes

  4. After 5 minutes

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Tap A rate = 1 / 37.5 = 2/75. Tap B rate = 1/45. Let B be open for x minutes. (2/75 + 1/45)x + (2/75)(30-x) = 1. (6/225 + 5/225)x + 2/75(30-x) = 1. (11/225)*x + 0.8 - (2/75)x = 1. (11/225 - 6/225)x = 0.2. (5/225)x = 0.2. x/45 = 0.2. x = 9.

AI explanation

Tap A runs for the full 30 minutes, filling 30/37.5 or 4/5 of the cistern, which leaves 1/5 of the cistern to be filled by tap B. Since tap B fills the tank in 45 minutes, its hourly rate is 1/45, and the time it needs to run to fill the remaining 1/5 is (1/5) / (1/45) = 9 minutes. Therefore, tap B must be turned off after 9 minutes to ensure the cistern is exactly full in half an hour.

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