Question

It takes an older pump 3 times as long to drain a certain pool as it does a newer pump. Working together, it takes the two pumps 9 hours to drain the pool. How long will it take the older pump to drain the pool working alone?

Answer 1

36hrs

Explanation:

Let the older pump be "a" and the newer pump be "b"

3a = b

3a + b = 9

We simply put the value of b from equation 1 into equation 2

3a + (3a) = 9

6a = 9

a = 1.5

If a = 1.5

3(1.5) = 4.5

b = 4.5

If a and b do it in 9hrs, it means they both contribute 4 parts to each hour's progress. 60minutes/4 = 15minutes a part.

So the new pump does in 15minutes what the old pump does in 45minutes

Ratio 3:1 = 4 NB: ratio 3 is for the new pump because it is 3 times as efficient.

So the old pump working alone will require 9*4 = 36hrs