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?
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?
Solution
To solve this problem, we first 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 work/4.5 hours = 0.2222 works/hour.
- B and C together can complete the work in 3 hours. So, their combined rate is 1 work/3 hours = 0.3333 works/hour.
- C and A together can complete the work in 2.25 hours. So, their combined rate is 1 work/2.25 hours = 0.4444 works/hour.
Now, if we add up the rates of (A+B), (B+C), and (C+A), we get 2*(A+B+C) = 0.2222 + 0.3333 + 0.4444 = 1 works/hour.
So, the combined rate of A, B, and C working together is 1/2 works/hour = 0.5 works/hour.
Therefore, to complete 1 work, they will take 1 work / 0.5 works/hour = 2 hours.
So, A, B, and C working together will take 2 hours to finish the piece of work.
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