Two pipes A and B together can fill a tank in 6 hours. If pipe A can fill 5 hours faster than pipe B, in how many hours pipe B alone can fill the tank?

Pipe A and B can fill the tank = 6 hours

Let
Pipe B can fill the tank in x hours
Pipe A will take x - 5 hours

Now
(1/x) + 1/(x - 5) = 1/6
(x - 5 + x)/x(x - 5) = 1/6
⇒ 6(x - 5 + x) = x² - 5x
⇒ 12x - 30 = x² - 5x
⇒ x² - 17x + 30 = 0
⇒ x² - 15x - 2x + 30 = 0
⇒ x(x - 15) - 2(x - 15) = 0
⇒ (x -15)(x - 2) = 0
x = 15 and x = 2

If x = 2, A = - 3 and time cannot be negative
So x = 15 hours
∴ B will fill the tank in 15 hours.