Please help. My homework is due tomorrow.

Question

Two pumps are filling a pool. One of them is high power and can fill the pool alone in 2 hours less time than the other can do so. Given that, working together, both pumps can fill the pool in 144 minutes, how long, in hours, will it take the powerful pump to fill the pool alone?

Answer 1

Let p = the time which the faster pump takes, then p + 2 is the time the slower pump takes.

The equation which describes this situation is

(1/p) + [1/(p+2)] = 12/5 which is the time (in hours) which is needed by both pumps together.

This equation resolves to a quadratic 5p² - 14p -24 for which the only usable root is p = 6/5.

Now the question always comes up: why is this equation is correct?

The answer is that the reciprocal of the time is a RATE, and the quantity of work to be done is "job", in this case "fill the pool". If that explanation isn't clear enough, please let me know.

Answer 2

144 minutes = 2 hour and 24 minutes = 2 and 24/60 = 2 and 2/5 = 12/5 hour

the combined work rate is 5/12.

the slower pump has work rate 1/R

the faster pump has work rate 1/(R-2)

1/R + 1/(R-2) = 5/12

12(R-2) + 12R = 5R(R-2)

12R - 24 + 12R = 5R^2 - 10R

24R - 24 = 5R^2 - 10R

0 = 5R^2 - 10R - 24R + 24

0 = 5R^2 - 34R + 24

0 = ( 5R - 4)(R - 6 )

5R - 4 = 0 ---> R = 4/5 ---> results in negative times.

R-6=0 ---> R = 6

The slower pump fills the pool in 6 hours.

The fast pump fills the poll in 4 hours.

Their combined work rate is 1/6 + 1/4 = 10/24 = 5/12