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 $\frac{2}{b-3}+\frac{2}b=1\Leftrightarrow b^2-7b+6=0\Leftrightarrow b=6\text{ or }b=-1$ hence $b=6$ and thus $a=3$.

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