Question
A and B together can complete a work in 10 days. B and C
together can do it in 12 days, and A and C together can do it in 15 days. In how many days will all three working together finish the work?Solution
Let total work = 1 unit. Rates: A + B = 1/10 work per day B + C = 1/12 A + C = 1/15 Add all three equations: (A + B) + (B + C) + (A + C) = 2(A + B + C) = 1/10 + 1/12 + 1/15 Find RHS: LCM of 10, 12, 15 = 60 1/10 = 6/60, 1/12 = 5/60, 1/15 = 4/60 Sum = (6 + 5 + 4)/60 = 15/60 = 1/4 So 2(A + B + C) = 1/4 ⇒ A + B + C = 1/8 work per day Time to finish 1 work together = 1 ÷ (1/8) = 8 days.
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