With both taps turned on, a tank can be filled in 24 minutes. With only one tap on, One of the taps takes twenty minutes longer than the other tap to fill the tank. How long does it take the faster tap to fill the tank by itslef.
x = faster tap
(x+20) = slower tap
1/x + 1/(x+20) = 1/24
x + 20 + x = (x^2+20x)/24
48x + 480 = x^2 + 20x
x^2 -28x-480 = 0 Use quadratic formula to find x = 40 min
Let the time of the faster one be "t"
then the time of the slower one is "t + 20".
Equation: [1/t] + [1/(t + 20)] = 1/24
Multiplying through by 24(t)(t + 20) ---> [24(t + 20)] + [24t] = [t(t + 20)]
24t + 480 + 24t = t2 + 20t
t2 - 28t - 480 = 0
(t - 40)(t + 12) = 0
t = 40 minutes
t + 20 = 60 minutes