Multiple choice

Pipes A, B, C and D can fill a tank with water in 15, 20, 30 and 60 hours, respectively. Pipe A is opened at 4 a.m., B at 5 a.m., C at 6 a.m. and D at 7 a.m. At what time is the tank completely full?

  1. 9:30 a.m.

  2. 10:00 a.m.

  3. 10:30 a.m.

  4. 11:00 a.m.

Reveal answer Fill a bubble to check yourself
D Correct answer
AI explanation

Assume the tank is full at 7 a.m. plus t hours. The combined work rate of pipes A, B, C and D is 1/15 + 1/20 + 1/30 + 1/60, which equals 12/60 or 1/5 per hour. The work done by each pipe equals its rate multiplied by its operating time: A works for (3 + t) hours, B works for (2 + t) hours, C works for (1 + t) hours, and D works for t hours. Setting the equation, (3+t)/15 + (2+t)/20 + (1+t)/30 + t/60 = 1, and multiplying by 60 yields 4(3+t) + 3(2+t) + 2(1+t) + t = 60. Simplifying gives 20 + 10t = 60, meaning t = 4. Since D opened at 7 a.m., adding 4 hours gives 11:00 a.m.