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ect the correct answerA and B working together, can do a piece of work in 4 1/2hours. B and C working together can do it in 3 hours. C and A working together can do it in 2 1/4hours. All of them begin the work at the same time. Find how much time they will take to finish the piece of work?Options3 hours2·5 hours2 hours3·25 hours

Question

ect the correct answerA and B working together, can do a piece of work in 4 1/2hours. B and C working together can do it in 3 hours. C and A working together can do it in 2 1/4hours. All of them begin the work at the same time. Find how much time they will take to finish the piece of work?Options3 hours2·5 hours2 hours3·25 hours

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Solution

To solve this problem, we first need to find the rates at which A, B, and C work.

  1. A and B can complete the work in 4.5 hours. So, their combined rate is 1/4.5 = 0.2222 work/hour.
  2. B and C can complete the work in 3 hours. So, their combined rate is 1/3 = 0.3333 work/hour.
  3. C and A can complete the work in 2.25 hours. So, their combined rate is 1/2.25 = 0.4444 work/hour.

Now, if we add up the rates of A and B, B and C, and C and A, we get 2*(A+B+C) = 0.2222 + 0.3333 + 0.4444 = 1 work/hour.

So, the combined rate of A, B, and C is 1/2 = 0.5 work/hour.

Therefore, to complete the work, they will take 1/0.5 = 2 hours.

So, the correct answer is 2 hours.

This problem has been solved

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