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?

let t equal the fill time

the pipes each fill a fraction of the pool
the fractions sum to one (the whole pool)

one fraction is t/8
the other is t/12

t/8 + t/12 = 1

24 is the LCD

3t + 2t = 24

4.8 hrs

Isnt five divided by 24 invalid?

I don't know because I need it for RSM

To find out how long it will take to fill the pool when both pipes are used simultaneously, you can use the concept of work rate.

The work rate of a pipe can be defined as the amount of work it can do in one unit of time. In this case, the work rate of the first pipe is 1 pool per 8 hours, and the work rate of the second pipe is 1 pool per 12 hours.

When both pipes are used simultaneously, their work rates are combined, so you can add them together to find the total work rate. So the total work rate when both pipes are used is 1/8 + 1/12 pools per hour.

To simplify this equation, you need to find a common denominator. The product of the denominators 8 and 12 is 96, so you can rewrite the equation as 12/96 + 8/96.

Now, add the numerators together and keep the common denominator: 12 + 8 = 20. The equation becomes 20/96.

To determine how long it will take to fill the pool, you can calculate the reciprocal of the work rate. The reciprocal of 20/96 is 96/20, which simplifies to 4.8.

Therefore, it will take approximately 4.8 hours to fill the pool if both pipes are used simultaneously.