Question

bobby and chuck are playing in the backyard, busily filling a big bucket with mud. They could fill the bucket together in 15 minutes. It would take Bobby 40 minutes to fill it alone. How long would it take Chuck to fill the bucket?

Answer 1

Explanation:

Let's assume that it takes Chuck x minutes to fill the bucket alone.

We know that Bobby can fill the bucket alone in 40 minutes, which means that in one minute, Bobby can fill 1/40 of the bucket.

We also know that Bobby and Chuck working together can fill the bucket in 15 minutes, which means that in one minute, they can fill 1/15 of the bucket together.

To find out how much of the bucket Chuck can fill in one minute, we can subtract Bobby's contribution from the combined contribution of both of them:

1/15 - 1/40 = 8/120 - 3/120 = 5/120

So we know that in one minute, Chuck can fill 5/120 of the bucket.

To find out how long it would take Chuck to fill the bucket alone, we can set up a proportion:

5/120 = 1/x

Cross-multiplying, we get:

5x = 120

x = 24

Therefore, it would take Chuck 24 minutes to fill the bucket alone.