Question

one pump can fill a swimming pool in 12 h. after it has been used for 4and a half hours, pipe B is also used, and the pool is filled in another 4 and a half hours. how long would it take to fill the pool with pipe b by itself

Answer 1

Pump A can fill the pool in 12 hours, so in 1 hour, it will fill 1/12 of the pool. In 4 1/2 hours, it will fill \(4 \frac{1}{2} * \frac{1}{12} = 3/8\) of the pool. That leaves 5/8 of the pool to be filled in 4 1/2 by both pump A and B working together.

5/8 = 4 1/2 * (1/12 + B)

Solve that for B to find the fraction of the pool pump B can fill in an hour. Then use that number to find out how many hours it would take for pump B to fill the pool by itself.

The general principle for these problems is to find out the unit rate, which is the amount each one does by itself in the relevant unit of time. If you write the equations as fractions of the whole, you don't need to know the total volume of the pool.