Question

A large pipe can fill a tank in 6 hours less than it takes the small pipe. Working together, they can fill it in `4` hours. How long would it take the small pipe to fill the tank if it was working alone?

Answer 1

Let the time it takes to fill the smaller pipe be `x` and the time it takes the larger pipe be `x - 6`.

Then, the amount of tank that can be filled in `1` hour is:

`1/x + 1/(x - 6) = 1/4`

Solve this equation.

`(4(x - 6))/(4x(x - 6)) + (4(x))/(4x(x - 6)) = (x(x - 6))/(4(x)(x - 6))`

We can now eliminate the denominators.

`4x - 24 + 4x = x^2 - 6x`

`0 = x^2 - 14x + 24`

`0 = (x - 12)(x - 2)`

`x = 12 and 2`

Two solutions may seem non sensical, but if you determine the length of time it takes using the large pipe, you will get `6` and `-4`. A negative answer is not possible, so we discredit `x = 2`.

So, it takes the small pipe `12` hours to fill the tank.

Hopefully this helps!