Jane needs to fill her pool with water. Ace said it will take them 40 minutes to fill the pool. Ben said it will take them 60 minutes to fill the pool. How long it will take for both Ace and Ben to fill the pool at the same time?

50 minutes. 40 ÷ 2 = 20 60 ÷ 2 = 30 30 + 20 = 50

I think you need to clarify who "them" is in each case.

To find out how long it will take for both Ace and Ben to fill the pool at the same time, we need to calculate their combined rate of filling the pool.

Ace can fill the pool in 40 minutes, which means his filling rate is 1 pool per 40 minutes.

Similarly, Ben can fill the pool in 60 minutes, so his filling rate is 1 pool per 60 minutes.

To find their combined filling rate, we add their individual rates:

Ace's rate + Ben's rate = 1/40 + 1/60

To add the fractions, we need a common denominator, which is the least common multiple (LCM) of 40 and 60. The LCM of 40 and 60 is 120.

Now, let's convert the fractions to have the same denominator:

Ace's rate + Ben's rate = (3/120) + (2/120) = 5/120

Simplifying this fraction, we get:

Ace's rate + Ben's rate = 1/24

So, when Ace and Ben work together, their combined filling rate is 1 pool per 24 minutes.

Therefore, it will take Ace and Ben 24 minutes to fill the pool together.