Discussion
If Ajay completes a certain work in 8 days and Vijay can complete the same work in 24 days, find the time in which the work will be completed if both Ajay and Vijay work together.
Answer: C
Work rates add when people work together.
\[ \text{Ajay's rate} = \frac{1}{8}, \qquad \text{Vijay's rate} = \frac{1}{24} \text{ of the job per day} \]
\[ \text{combined} = \frac{1}{8} + \frac{1}{24} = \frac{3 + 1}{24} = \frac{1}{6} \]
\[ t = 6 \text{ days} \]
Averaging the two times to 16 days is wrong: rates add, times do not. The joint time must always be less than the faster worker's 8 days.
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