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?

See previous post.

This is dumb!

To solve this problem, we can use the concept of "work rates." The work rate of a pipe represents the amount of work it can do in a given unit of time. In this case, filling the pool can be considered as work.

Let's start by calculating the work rates of each pipe:
- The inlet pipe can fill the pool in 24 hours. So, its work rate is 1 pool/24 hours.
- The drain pipe can empty the pool in 40 hours. So, its work rate is -1 pool/40 hours (negative because it's emptying the pool).

Since the pool is already one-third filled, we can consider it as 1/3 of the work done. So, the remaining work to fill the pool is 1 - 1/3 = 2/3.

Now, let's denote the time it takes to fill the pool after the drain pipe is accidentally opened as "t" hours. During this time, the inlet pipe is working, but the drain pipe is also working against it.

The combined work rate of both pipes is the sum of their individual work rates:
- For the inlet pipe, the work rate is 1 pool/24 hours.
- For the drain pipe, the work rate is -1 pool/40 hours.

Using the concept of work rates, we can set up the equation:
(1/24 - 1/40) pools/hour * t hours = 2/3 pool

Now, let's solve for "t":

(1/24 - 1/40) * t = 2/3

First, let's find a common denominator for 24 and 40, which is 120:

(5/120 - 3/120) * t = 2/3

(2/120) * t = 2/3

Now, let's simplify the equation:

(1/60) * t = 2/3

Next, let's multiply both sides by 60 to isolate "t":

t = (2/3) * 60

t = 40

So, after the drain pipe is accidentally opened, it will take 40 hours to fill the pool completely.