Jasper is filling a nest, it takes him 20 mins. Mr. S is removing paper from the nest which takes him 25 mins. How long will Jasper take to fill the nest if Mr. S emptying the nest at the same time.

Question

If tried various ways but can't seem to get the answer

Answer 1

At first I thought you needed the container size, but it doesn't matter.

Since it takes 20 minutes for Jasper to fill, and 25 minutes for Mr. S to empty, Jasper's fill rate = 1/20 container per minute. Mr. S empty rate = 1/25 container per minute. So the equation would be:

(1/20 * Time) - (1/25 * Time) = 1.

Why 1? Because the whole container filled is 1. Until filled, it is 1/100 filled, 1/50 filled, 1/10 filled, etc. A fully filled container is size 1 - regardless of the original container size (could be cm, m, miles, ft, etc.).

Also, you don't need to worry about units, since they all cancel out.

The reduces to 0.01 * Time = 1. Or if you want to keep as a fraction, 1/100 * Time = 1. Then multiply both sides by 100 to get Time = 100. So in 100 minutes, the container will be filled regardless of the size.

Answer 2

The equation you need is

(1/20) - (1/25) = 1/T which can be solved to find T = 100

Now why is that equation correct? The terms which look like reciprocals are RATES!

What this means is that 1/100 of the nest is filled per minute.

If that is still unclear, send me a message & I will try to help further.