Rate Problem

Question

One 10-hp pump can fill the backyard pool in 16 hours and a more powerful pump can fill the same pool in 13 hours. The 10-hp pump has been filling the pool for 5 hours before the second more powerful pump is also used to fill the pool. Now the two pumps are working together to fill the pool. What's the total number of hours that the 10-hp pump has spent filling the pool?Don't round your answer.

Answer 1

This is a rate problem.

 

Let r = the rate of filling the pool by the 10-hp pump,

 

R = the rate of filling the pool by the more powerful pump, and

 

V = the volume of the pool.

 

r = V/16

 

R = V/13

 

In 5 hours, the 10-hp pump has managed to fill 5/16 of the pool.  The remaining 11/16 of the pool is pumped by both.

 

time = volume / rate

 

time = (11V/16) / (V/16 + V/13)

 

= (11/16) / (1/16 + 1/13)

 

= 4.93 hours

 

The 10-hp pump works for 5 + 4.93 = 9.931 hours.