Question

Aaron alone can finish a piece of work in 12 days and Brandon alone can do it in 15 days. If both of them work at it together, how much time will they take to finish it?​

Answer 1

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Aaron alone can finish a piece of work in 12 days and Brandon alone can do it in 15 days. If both of them work at it together, how much time will they take to finish it?

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$\small\tt{Time\:taken\:by \:Aaron\: to\: finish\: the\: work\: =\: 12 \:days.}$

$\small\tt{Work\:done \:by \:Aaron\: in\: 1\: day\: = \:{\frac{1}{12}}}$

$\small\tt{Time\:taken\:by \:Brandon\: to\: finish\: the\: work\: =\: 15\: days.}$

$\small\tt{Work\:done \:by \:Brandon\: in\: 1\: day\: = \:{\frac{1}{15}}}$

$\small\tt{Work \:done\: by \:(Aaron + Brandon) \:in \:1 day\:}\\{\small\tt{\: =\:{\frac{1}{13}} +{\frac{1}{15}} \: = \:{\cancel\frac{9}{60}}\:=\:{\frac{ 3}{20}}}}$

$\small\tt{Time\:taken\: by\: (Aaron + Brandon)\:to\: }\\{\small\tt{finish\: the\: work\:}}$

$\small\tt{ \:=\:{\frac{20}{3}}\:\:days,}$

$\small\tt{ i.e,\:\:6{\frac{2}{3}}\:days.}$

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$\small\tt{Hence\: both\: can \:finish\: the\: work\: in\:6{\frac{2}{3}} \: days.}$

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$\bf\purple{\underline{\boxed{Thanks}}}$

Answer 2

Time taken by Aaron to finish the work = 12 days.

Work done by Aaron in 1 day = 1/12

Time taken by Brandon to finish the work = 15 days.

Work done by Brandon in 1 day = 1/15

Now , Work done by both in 1 day = 1/12+1/15 = 3/20

Time taken = 20/3 days.