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If A can do a piece of work in 10 days and B can do the same work in 15 days, how long will they take to complete it together?

Question

If A can do a piece of work in 10 days and B can do the same work in 15 days, how long will they take to complete it together?

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Solution

First, we need to find out how much work A and B can do in one day.

A can complete the work in 10 days, so A can do 1/10 of the work in one day. B can complete the work in 15 days, so B can do 1/15 of the work in one day.

To find out how much work they can do together in one day, we add the fractions together:

1/10 + 1/15 = 1.5/15 + 1/15 = 2.5/15 = 1/6

So, together, A and B can do 1/6 of the work in one day.

To find out how many days they would take to complete the work together, we take the reciprocal of 1/6, which is 6.

So, A and B together can complete the work in 6 days.

This problem has been solved

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