Question

Two taps, having different rates of flow are used to fill a large water tank. If tap A is used on its own it will take 5 hours longer to fill the tank that it would take tap B to fill it on its own. Together, the taps would fill the tap in 6 hours. Assuming that the taps are running at full capacity

Answer 1

Oh and the qn is How long will it take tap A to fill the tank

how long will it take tap B to fill the tank
help

Answer 2

Tap B = X hrs.
Tap A = (X + 5) hrs.

1/X + 1/(X + 5) = 1/6,
Multiply both sides by common denominator, x(x + 5):
x + 5 + x = x(x + 5) / 6,
Multiply both sides by 6:
6x + 30 + 6x = x(x + 5),
12x + 30 = x^2 + 5x,
Combine like-terms and set Eq = to 0:
-x^2 + 7x + 30 = 0,
Multiply both sides by -1,:
x^2 + 7x + 30 = 0,
Factor Eq:
(x + 3) (x - 10) = 0,
x + 3 = 0, x = -3,
x - 10 = 0, x = 10.
Select positive value:
x = 10 hrs = tap B HRS,
X + 5 = 10 + 5 = 15hrs = 15 = Tap A hrs.