Question

Two taps A and B fill a swimming pool together in two hours. Alone, it takes tap A three hours less than B to fill the same pool. How many hours does it take each tap to fill the pool separately?

Answer 1

a=b-3

2/)b-3)+2/b=1

a=3 hours

b=6 hours

Answer 2

Let's call
`a` the number of hours it takes for A to fill the pool and
`b` the number of hours it takes for B to fill the pool.

We have
`a=b-3` and
`\frac{2}a+\frac{2}b=1` hence
`(2)/(b-3)+\frac{2}b=1\Leftrightarrow b^2-7b+6=0\Leftrightarrow b=6\text{ or }b=-1` hence
`b=6` and thus
`a=3`.


`\boxed{b=6,a=3}`