Question

When two pipes fill a pool together, they can finish in 4 hours. If one of the pipes fills half the pool, then the other takes over and finishes filling the pool, it will take them 9 hours. How long will it take each pipe to fill the pool if it were working alone?

a. One pipe takes 6 hours alone, and the other takes 12 hours alone.
b. One pipe takes 8 hours alone, and the other takes 16 hours alone.
c. One pipe takes 5 hours alone, and the other takes 10 hours alone.
d. One pipe takes 7 hours alone, and the other takes 14 hours alone.

Answer 1

One pipe takes 12 hours alone, and the other takes 6 hours alone.

Step-by-step explanation:

Let's assume that the rate at which the first pipe fills the pool alone is x of the pool per hour. Since the other pipe fills the remaining half of the pool, its rate of filling is 2x of the pool per hour.

Together, they can fill the pool in 4 hours, so their combined rate is 1/4 of the pool per hour. We can set up the equation:

x + 2x = 1/4

Combining like terms, we get:

3x = 1/4

Dividing both sides by 3, we find that:

x = 1/12

Therefore, the first pipe takes 12 hours to fill the pool alone, and the second pipe takes 6 hours to fill the pool alone.