Algebra word problem

Question

It takes a smaller hose 3 times as long to fill a small swimming pool as it does a larger hose. It takes both hoses working together 15 minutes to fill the swimming pool. How long will it take the smaller hose to fill the pool by itself? Do not do any rounding.

Answer 1

If you think carefully about this, you might be able to arrive at the answer intuitively.

 

However, with situations like this, you can generally anticipate that you are going to end up with two formulas, and will make a substitution from one into the other.

 

If it takes the smaller hose 3 times as long to fill the pool as the larger hose, then we could say that the flow rate of the larger hose is 3x that of the smaller. When working together, they have a total flow rate of 4x the flow rate of the small hose alone. Let's say that s = small hose flow rate, and V is the pool volume. This being the case:

 

For both hoses together:

 

time to fill pool = pool volume / total flow rate

15 minutes = V / (3s + s)

s = V / (4 x 15) = V / 60  <-- this is going to be used, below

 

For the single small hose:

 

time to fill pool = V / s

Now substitute for s from above

time = V / (V / 60)

     = 60 minutes