Physics 205, Physics 215, Astronomy 211 - A swimming pool can be filled with two water pipes. Pipe A alone is able to fill the pool in one hour. Pipe B alone is able to fill the pool in two hours. Pipes A and B together are able to fill the pool in
(a) 1.5 h
(b) 30 min
(c) 20 min
(d) 40 min
(e) 3 h.
Answer. Choice (d) is the correct one.
The explanation is as follows. Pipe A pumps water at the rate 1 pool/hour. Pipe B pumps water at the rate 1 pool/( 2 hour) = 0.5 pool/hour. The two pipes together pump water at the rate 1.5 pool/hour.
If x hour are required to fill one pool with both pipes, then we must have the equation
Thus, cancelling the units on both sides, we get the equation
This equation has the solution x = 2/3. Since we were working with hours as time unit, the time required for both pumps together to fill the pool is (2/3) hour or 40 min.