Question

Two taps of various or different diameter can fill a tank in 9 and 3/8 hours. The tap of larger diameter takes 10 hrs less than the smaller one to fill the tank separately.Find the time in which each tap can separately fill the tank.

Answer 1

time taken by larger diameter tap --- x hrs
time taken by smaller diameter tap ---x + 10 hrs

combined rate = 1/x + 1/(x+1) = (2x+10)/(x(x+10))

(2x+10)/(x(x+10)) = 1/(75/8) = 8/75
8x^2 + 80x = 150x + 750
8x^2 - 70x - 750 = 0
(x-15)(8x + 50) = 0
x = 15 or x = some negative, which we'll reject

Time for the larger tap is 15 hrs
time for the smaller tap is 25 hrs

check:
combined rate = 1/15 + 1/25 = 8/75
time at combined rate = 1/(8/75) = 75/8 or 9 3/8 hrs