If A and B together can complete a work in 18 days, A and C together in 12 days and B and C together in 9 days, then B alone can do the work in ____?
Answer: 24 days
Explanation
Using the concept of work and rate, we can analyze the given information:
A+B = 1/18 (work done per day)
A+C = 1/12
B+C = 1/9
By adding the first two equations, we get:
(A+B) + (A+C) = 1/18 + 1/12
2A + (B+C) = 1/6
2A + 1/9 = 1/6
2A = 1/6 - 1/9
2A = 1/18
A = 1/36 (work done by A per day)
Now, we can find B's work per day:
B = 1/18 - 1/36 = 1/24
So, B alone can do the work in 24 days.
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