One pipe can fill a swimming pool in 8 hours.
Another pipe takes 12 hours. How long will it take to fill the pool if both pipes are used simultaneously?
Pipe A will fill 1/8 of the pool is 1 hour. Pipe B will fill 1/12 of the pool in 1 hour.
So, 1/8 + 1/12 = 5/24
It will take 4.8 hours to fill the pool.
To find out how long it will take to fill the pool when both pipes are used simultaneously, we can use the concept of work rate.
Let's say the swimming pool has a certain capacity, measured in units of work (let's call it "W"). The first pipe can fill the pool in 8 hours, which means it has a work rate of W/8 per hour. Similarly, the second pipe has a work rate of W/12 per hour.
When both pipes are used simultaneously, their work rates add up. So, the combined work rate is (W/8 + W/12) per hour.
To calculate the time it takes to fill the pool, we can use the formula t = W/rate, where t is the time in hours, W is the work to be done, and rate is the work rate.
In this case, we want to find the time it takes to fill the pool, so let's set the work to be done as W and the combined rate as (W/8 + W/12). Plugging these values into the formula, we get:
t = W / (W/8 + W/12)
To simplify this equation, we need to find a common denominator for the two fractions in the denominator:
t = W / ((3W + 2W) / (3 * 8))
Simplifying further:
t = W / (5W / 24)
t = 24 / 5
Therefore, it will take 4.8 hours (or 4 hours and 48 minutes) to fill the swimming pool if both pipes are used simultaneously.