Expert: Sherman D. - 9/23/2009

Question
Two pumps of different sizes, working together, can empty a fuel tank in 5 hours.  The larger pump can empty this tank in 4 hours less than the smaller one.  If the Larger one is out of order, how long will it take the smaller one to do the job alone


Answer
(1/x) + (1/y) = (1/5)

(1/(y - 4)) + (1/y) = (1/5)

5y + 5(y - 4) = y(y - 4)
5y + 5y - 20 = y^2 - 4y
y^2 - 4y = 10y - 20
y^2 - 14y + 20 = 0

y = (14 +/- sqrt((-14)^2 - 4(1)(20)))/(2(1))
y = (14 +/- sqrt(116))/2
y = (14 +/- 2sqrt(29))/2
y = 7 +/- sqrt(29)

x = 3 +/- sqrt(29)

since you can't have negative time.

it would take about 12.385 hours