omar2oxford
Answered

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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?

Sagot :


a=b-3

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

a=3 hours

b=6 hours

Hippalectryon
Let's call [tex]a[/tex] the number of hours it takes for A to fill the pool and [tex]b[/tex] the number of hours it takes for B to fill the pool.

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

[tex]\boxed{b=6,a=3}[/tex]
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