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Two worker A and B are engaged to do a piece of work. A working alone would take 8 hours more to complete the work that when work together. If B worked alone, would take $${\text{4}}\frac{1}{2}$$ hours more than when working together. The time required to finish the work together is = ?

Correct Answer: 6 hours
$$\eqalign{ & {\text{Let,}} \cr & {\text{a}} = {\text{8h}} \cr & {\text{b}} = {\text{4}}\frac{1}{2}{\text{h}} = \frac{9}{2}{\text{h}} \cr} $$
Time required to finish the work together
$$\eqalign{ & = \sqrt {{\text{ab}}} \cr & = \sqrt {8 \times \frac{9}{2}} \cr & = 6{\text{ h}} \cr} $$

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