A reservoir is provided by two pipes A and B. A can fill the reservoir 5 hours…

Answer: 10 hours

Let the time taken by the slower pipe be x hours. Since the faster pipe fills 5 hours faster, its time is x - 5 hours.

Their combined rate is 1/(x - 5) + 1/x, and this equals 1/6 (together they fill the reservoir in 6 hours).

Set up the equation: 1/(x - 5) + 1/x = 1/6.

Solve the equation: combine fractions to get (2x - 5)/(x(x - 5)) = 1/6, which leads to x^2 - 17x + 30 = 0.

Factor the quadratic: (x - 15)(x - 2) = 0, so x = 15 or x = 2.

If x = 2 the faster pipe would take x - 5 = -3 hours, which is impossible, so discard x = 2. Thus x = 15 hours for the slower pipe.

Therefore the faster pipe takes 15 - 5 = 10 hours.

Quick check: 1/10 + 1/15 = 1/6, so the answer is correct.