Working together, two pumps can drain a certain pool in 6 hours. If it takes the older pump 15 hours to drain the pool by itself, how long will it take the newer pump to drain the pool on its own?

Question

College Math Help. Dealing with time. Its a homework problem I'm struggling with.

Answer 1

Taking the information given and letting P_n = pumping rate of the new pump and

P_o = pumping rate of the old pump (both in gallons/hour)

Now, let's assume that the pool has 3000 gallons (This is arbitrary... could be any reasonable number)

Then 6P_n + 6P_o = 3000

and 15P_o = 3000

So,

P_o = 200 gpm

Substiting back in the other equation, we find that

P_n = 300 gpm