A Chinese restaurant has a large goldfish pond.

Question

Suppose that an inlet pipe and a hose together can fill the pond in 10 hrs. The inlet pipe alone can complete the job in one hour less time than the hose alone. Find the time that the hose can complete the job alone and the time that the inlet pipe can complete the job alone.

Answer 1

Let's assume that the pond is 1000 gallons (This number is arbitrary... could be any reasonable number)

Let P = the pipe flow rate

H = the hose flow rate

T = Time for the individual hoses can fill the pond

Then,

10P + 10H = 1000 or P + H = 100

and HT = P(T-1) = 1000 H = 1000/T and P = 1000/(T-1)

So, 1000/(T-1) + 1000/T = 100 Solving for T we find that T = 20.51 or .49 (This value not possible!)

Therefore, T = 20.51 hours So, H = 1000/T = 48.75 gph & P = 1000/(T-1) = 51.25 gph

So, the time for each to fill alone is....... H: 1000/48.75 = 20.51 hours P: 1000/(51.25) = 19.51 hours