PROBLEM

Suppose a swimming pool has two intake pipes. One pipe fills the pool in 10 hours and the other in 15 hours. If both pipes are open, how long will it take to fill the pool?

SOLUTION

If we let x be the number of hours it takes for both pipes to fill the pool, then in 1 hour the first pipe will fill of the pool, the second pipe will fill of the pool, an the two pipes together will fill of the pool. So we must have

CHECKING

In 6 hours the first pipe will fill of the pool and the second pipe will fill of the pool. Thus in 6 h the two pipes together will fill

of the pool; that is, the entire pool.

ANSWER

• The two pipes together will fill the pool in 6 hours.