Discussion
Two men can do a piece of work in 6 hrs. and 4 hrs. respectively. After the first has worked for 2 hrs. he is joined by the other. Then the time taken to complete the work will be
Answer: A
The work is completed 1.6 hrs. after the second man joins.
The first man does \(\frac{1}{6}\) of the work per hour and the second \(\frac{1}{4}\). In his first 2 hours alone the first man does \(\frac{2}{6} = \frac{1}{3}\), leaving \(\frac{2}{3}\) for the two together:
\[ \begin{aligned} \text{joint rate} &= \frac{1}{6} + \frac{1}{4} = \frac{5}{12} \\ \text{time} &= \frac{2}{3} \div \frac{5}{12} = \frac{8}{5} = 1.6\ \text{hrs} \end{aligned} \]
The question asks for the time taken after the two start working together; counting the first man's 2 hours as well would give 3.6 hours, which is not offered. 2.4 hours is how long the two together would need for the whole job.
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