Aresorvoir can be filled by an inlet pipe in 24 hours and emptied by an outlet pipe 28 hours. the foreman starts to fill the resorvoir, but he forget to close the outlet pipe. six hours later he remembers and closes the outlet. how long does it take altogether to fill the reservoir? show your solution?

The flow rate of water into the reservoir is 1 reservoir per 24 hours. The flow rate out is one reservoir per 28 hours. For the six hours when the outlet pipe was open, the reservoir was filling at a rate of (1/24) - (1/28) = (7/168) - (6/168) = 1/168 reservoir per hour. Multiplied by 6 hours, this equals a total of 1/28 reservoir during the time the outlet pipe was left open.

The remaining volume of the reservoir will be filled at a rate of 1/24 reservoir per hour. What we need to do, then, is find the number of 1/24 reservoir portions in 27/28 reservoir. (27/28) = (162/168) = (23.142857/24). The entire reservoir, then will take 23.142857 + 6 = 29.142857 hours to fill.

The answer is c. 7 (i think) i’m almost sure though