A and B can do a piece of work in 12 days and 39 days, respectively. Both work for 4 days and then A leaves. How long (in days) will B take to complete the remaining work?
22
A's one-day work \(= \frac{1}{12}\) and B's one-day work \(= \frac{1}{39}\).
Combined one-day work \(= \frac{1}{12} + \frac{1}{39} = \frac{13 + 4}{156} = \frac{17}{156}\).
Work done together in 4 days \(= 4 \times \frac{17}{156} = \frac{68}{156} = \frac{17}{39}\).
Remaining work \(= 1 - \frac{17}{39} = \frac{22}{39}\).
Time for B alone \(= \frac{22}{39} \div \frac{1}{39} = \frac{22}{39} \times 39 = 22\) days.
Hence, B takes 22 days to finish the remaining work.
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