Select 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?Options2 hours3 hours2·5 hours3·25 hours
Question
Select 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?Options2 hours3 hours2·5 hours3·25 hours
Solution
To solve this problem, we need to find the rate at which A, B, and C work together.
- A and B can complete the work in 4 1/2 hours, so their combined rate is 1/(4.5) = 0.2222 work/hour.
- B and C can complete the work in 3 hours, so their combined rate is 1/3 = 0.3333 work/hour.
- C and A can complete the work in 2 1/4 hours, so their combined rate is 1/(2.25) = 0.4444 work/hour.
If we add these three rates together, we get 0.2222 + 0.3333 + 0.4444 = 1 work/hour. However, this is the rate for two workers working together, and we have counted each worker twice. So, the rate for all three workers working together is 1/2 = 0.5 work/hour.
Therefore, to complete 1 work, they will need 1/0.5 = 2 hours.
So, the correct answer is 2 hours.
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