Question

Two pipes together can fill a tank in 12 hours. If the first pipe can fill the tank 10 hours faster than the second then how many hours will the second pipe take to fill the tank?

Answer 1

Given:

Two pipes together fill the tank in 12 hours.

The first pipe is 10 hours faster than the second.

Step-wise calculation:

1. Let the time for the second pipe = x hours.

Then the first pipe = (x – 10) hours.

2. Combined rate: `1/x + 1/(x - 10) = 1/12`.

3. Solve: `(x - 10 + x)/(x(x - 10)) = 1/12`

⇒ `(2x - 10)/(x^2 - 10x) = 1/12`

⇒ 12(2x – 10) = x² – 10x 

⇒ 24x – 120 = x² – 10x

⇒ x² – 34x + 120 = 0

4. Quadratic formula/factor (or compute discriminant):

D = 34² – 4 × 1 × 120 

= 676

= 26²

Roots: `x = (34 ± 26)/2` 

⇒ x = 30 or x = 4

5. x = 4 gives first pipe = x – 10 = –6 (impossible), so reject x = 4.

The second pipe takes 30 hours to fill the tank.