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
