A 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 hours3·25 hours2 hours
Question
A 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 hours3·25 hours2 hours
Solution 1
To solve this problem, we need to find the rates at which A, B, and C work.
- A and B together can complete the work in 4.5 hours. So, their combined rate is 1/4.5 = 0.2222 work/hour.
- B and C together can complete the work in 3 hours. So, their combined rate is 1/3 = 0.3333 work/hour.
- C and A together 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 twice the total rate of A, B, and C. So, the total rate of A, B, and C is (0.2222 + 0.3333 + 0.4444) / 2 = 0.5 work/hour.
Therefore, all of them working together can complete the work in 1/0.5 = 2 hours. So, the correct answer is 2 hours.
Solution 2
To solve this problem, we need to find the rates at which A, B, and C work.
- A and B together can complete the work in 4.5 hours. So, their combined rate is 1/4.5 = 0.2222 work/hour.
- B and C together can complete the work in 3 hours. So, their combined rate is 1/3 = 0.3333 work/hour.
- C and A together 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 twice the total rate of A, B, and C. So, the total rate of A, B, and C is (0.2222 + 0.3333 + 0.4444) / 2 = 0.5 work/hour.
Therefore, A, B, and C together can complete the work in 1/0.5 = 2 hours. So, the correct answer is 2 hours.
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