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Select the correct answerA can do a piece of work in 8 days and B can do it in 10 days separately. How many days would it take for both A and B to finish the same work together?Options33/841/1042/1140/9

Question

Select the correct answerA can do a piece of work in 8 days and B can do it in 10 days separately. How many days would it take for both A and B to finish the same work together?Options33/841/1042/1140/9

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Solution

To solve this problem, we first need to find the rate at which A and B can complete the work.

  1. A can complete the work in 8 days, so A's rate of work is 1/8 of the work per day.
  2. B can complete the work in 10 days, so B's rate of work is 1/10 of the work per day.

When A and B work together, their rates of work are added. So, the combined rate of A and B is 1/8 + 1/10 = 5/40 + 4/40 = 9/40 of the work per day.

Therefore, to find out how many days it would take for both A and B to finish the work together, we divide the total work (which is 1) by their combined rate, which is 9/40.

So, the time it would take is 1 / (9/40) = 40/9 days.

So, the correct answer is 40/9.

This problem has been solved

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