Question

It takes 12 hours to fill a pool with the lids pipe; it can be emptied in 15 hours with the outlet pipe. If the pool is three over four full to begin with, how long will it take to fill it from there if both pipes are open?

a) Various time values
b) 6 hours
c) 7.5 hours
d) 8 hours

Answer 1

To fill the pool from three over four full if both pipes are open, it will take 15 minutes or 0.25 hours.

Step-by-step explanation:

To solve this problem, we need to find the combined rate at which both pipes fill the pool and then use that rate to calculate the time it takes to fill the pool from three over four full.

The rate at which the lid pipe fills the pool is 1/12 of the pool per hour, while the rate at which the outlet pipe empties the pool is 1/15 of the pool per hour. To find the combined rate, we subtract the rate at which the outlet pipe empties from the rate at which the lid pipe fills: 1/12 - 1/15 = 5/60 - 4/60 = 1/60 of the pool per hour.

Since the pool is already three over four full, it is 3/4 of the pool. To find the time it takes to fill the pool from three over four full, we divide the remaining portion of the pool (1 - 3/4) by the combined rate: (1 - 3/4) / (1/60) = 1/4 / (1/60) = 15 minutes or 0.25 hours.

Therefore, it will take 15 minutes or 0.25 hours to fill the pool from three over four full if both pipes are open.