A and B together can do a job in 6 days. A alone does it in 9 days. In how many days can B alone do it?
18 days
Treat the whole job as 1 unit of work and convert each person's speed into work done in one day.
A and B together finish in 6 days, so their combined one-day work \(= \dfrac{1}{6}\).
A alone finishes in 9 days, so A's one-day work \(= \dfrac{1}{9}\).
B's one-day work is what remains: \(\dfrac{1}{6} - \dfrac{1}{9}\). Using the common denominator 18, \(= \dfrac{3}{18} - \dfrac{2}{18} = \dfrac{1}{18}\).
If B does \(\dfrac{1}{18}\) of the job each day, B needs the reciprocal, \(18\) days, to complete the whole job.
Key concept: one-day work rates add and subtract directly, and time taken alone is the reciprocal of the one-day rate.
Hence B alone can finish the job in 18 days.
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