Discussion
A can do a piece of work in 40 days and B can do it in 60 days. In how many days will they finish the work, both working together?
Answer: C
They finish in 24 days. In one day A does 1/40 of the work and B does 1/60.
\[ \frac{1}{40} + \frac{1}{60} = \frac{3 + 2}{120} \]\[ = \frac{1}{24} \]So the work takes 24 days together. 30, 32 and 25 days are wrong because working together must be faster than A alone, and 25 days would need a combined rate of 1/25.
Check with a total of 120 units of work: A does 3 units a day and B does 2, so together they do 5 units a day, and 120 / 5 = 24 days. This also shows the answer is shorter than either person's time alone, which is a quick test for combined-work questions.
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