An inlet pipe on a swimming pool can be used to fill the pool in 24 hours. The drain pipe can be used to empty the pool in 40 hours. If the pool is one-third filled and then the drain pipe is accidentally opened, how long will it take to fill the pool?

___________ hours

225 40 hours

40 hour

To solve this problem, we will first determine the rate at which the inlet pipe and the drain pipe can fill or empty the pool, respectively.

Let's start by finding the filling rate of the inlet pipe. We know that it can fill the pool in 24 hours. Therefore, the rate at which the inlet pipe fills the pool is 1 pool / 24 hours, or 1/24 pools per hour.

Next, let's determine the rate at which the drain pipe empties the pool. We are given that it can empty the pool in 40 hours. This means that the drain pipe empties at a rate of 1 pool / 40 hours, or 1/40 pools per hour.

Now, let's calculate the rate at which the pool is filled or emptied based on the combination of the inlet and drain pipes. Since the drain pipe is accidentally opened, it will empty the pool as long as it is open.

When the pool is one-third filled, it means that it is filled with 1/3 of its total volume. Therefore, the remaining volume to be filled is 2/3 of the pool.

Considering the inlet pipe is filling the pool at a rate of 1/24 pools per hour and the drain pipe is emptying the pool at a rate of 1/40 pools per hour, the net filling rate is:

Filling rate - Draining rate = 1/24 - 1/40 = 5/120 - 3/120 = 2/120 = 1/60 pools per hour.

Now, to find out how long it will take to fill the remaining 2/3 of the pool, we need to divide this volume by the net filling rate:

(total volume to fill) / (net filling rate) = (2/3 pools) / (1/60 pools per hour)

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:

(2/3 pools) * (60 pools per hour / 1) = (2*60) / 3 = 120/3 = 40 hours.

Therefore, it will take 40 hours to fill the pool when the drain pipe is accidentally opened.