A can complete a task in 18 days, while B can finish the same task in half the time taken by A. If they work together, how much of the task can they complete in one day?

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Accepted Answer

A's one-day work is calculated as $$ \frac{1}{18} $$, since A can complete the task in 18 days. B can finish the same task in half the time taken by A, which is 9 days, so B's one-day work is $$ \frac{1}{9} $$.

When working together, their combined one-day work is the sum of their individual one-day work:  
$$
	ext{Combined Work} = \frac{1}{18} + \frac{1}{9}
$$

Taking the LCM of 18 and 9 gives 18:  
$$
	ext{Combined Work} = \frac{1}{18} + \frac{2}{18} = \frac{3}{18} = \frac{1}{6}
$$

Thus, A and B together can complete $$ \frac{1}{6} $$ of the task in one day.

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