A can complete a task in 10 days and, B can finish a task in 15 days, respectively. A starts the work and works for 4 days, after which B joins A. How many more days will they take to complete the task?
3.6 days
Work problems are solved through one-day work rates that can be added when people work together.
A's one-day work \(= \frac{1}{10}\) and B's one-day work \(= \frac{1}{15}\) of the task.
A works alone for 4 days first, completing \(4 \times \frac{1}{10} = \frac{4}{10} = \frac{2}{5}\) of the task.
Remaining work \(= 1 - \frac{2}{5} = \frac{3}{5}\).
Once B joins, their combined one-day work \(= \frac{1}{10} + \frac{1}{15} = \frac{3 + 2}{30} = \frac{5}{30} = \frac{1}{6}\).
Time to finish the rest \(= \frac{\text{remaining work}}{\text{combined rate}} = \frac{3/5}{1/6} = \frac{3}{5} \times 6 = \frac{18}{5} = 3.6\) days. The concept is adding rates, then dividing leftover work by the joint rate.
Hence they need 3.6 days more.
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