A man can do a certain task in 21 hours, another can do the task in 28 hours, and a boy can do the task in 48 hours. How long will it take to do the task if all work together?
Every hour man 1 does $\displaystyle \frac{1}{21}$ of the job, man 2 does $\displaystyle \frac{1}{28}$ of the job, and the boy does $\displaystyle \frac{1}{48}$ of it.
So that means, every hour $\displaystyle \frac{1}{21} + \frac{1}{28} + \frac{1}{48}$ of the job gets done
$\displaystyle = \frac{5}{48}$.
So if we set up a ratio (amount of job : hours)...
$\displaystyle \frac{5}{48} : 1$
$\displaystyle 5 : 48$
$\displaystyle 1 : \frac{48}{5}$
$\displaystyle 1 : 9.6$.
So they will finish the job in $\displaystyle 9.6$ hours, or 9 hours 36 mins.