Pipe b can fill a pool in 9 hours. The amount of time it takes pipe c to fill the same pool is unknown. When pipes b & c are both open, the pool can be filled in 4 hours. If pipe c is filling the pool by itself how many hours will it take

Answer: it will take pipe c 7.2 hours to fill the pool.

Step-by-step explanation:

Let t represent the number of hours it will take pipe c to fill the pool alone. It means that the rate at which pipe c fills the pool per hour is 1/t

Pipe b can fill a pool in 9 hours. It means that the number of hours it takes pipe b to fill the pool alone per hour is 1/9

By working together, they would work simultaneously and their individual rates are additive. When pipes b & c are both open, the pool can be filled in 4 hours. It means that the rate at which both pipes fill the pool per hour is 1/4. Therefore,

1/t + 1/9 = 1/4

(9 + t) / 9t = 1/4

Cross multiplying, it becomes

4 (9 + t) = 9t

36 + 4t = 9t

9t - 4t = 36

5t = 36

t = 36/5

t = 7.2 hours