Question : P, Q, and R alone can complete a piece of work in 30 hours, 10 hours and 15 hours respectively. In how much time will they finish the work if they work together?
Option 1: 5 hours
Option 2: 4 hours
Option 3: 8 hours
Option 4: 10 hours
Correct Answer: 5 hours
Solution :
The rate at which P, Q, and R work is $\frac{1}{30}$, $\frac{1}{10}$, and $\frac{1}{15}$ of the work per hour, respectively.
When they work together, their combined rate is $ = \frac{1}{30} + \frac{1}{10} + \frac{1}{15} = \frac{1}{5}$ of the work per hour
$\therefore$ The time it takes for them to finish the work together is the reciprocal of their combined rate $= \frac{1}{\frac{1}{5}} = 5$ hours
Hence, the correct answer is 5 hours.
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