A and B do a piece of work in 12 days, B and C in 15 days,and C and A in 20 days. how much time will A alone take to finish the wrk?
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Assuming everybody works at constant rate and independent from each other.
When A works for 5 days and B works for 7 days, we can conclude that A and B work together for 5 days and B works alone for 2 days. And
Work Rate(A+B) = 1/12 (work/day)
Thus, Work is done by A and B for 5 days together = 5 days x 1/12 (work/day) = 5/12 work
When B works for 7-5 = 2 days and C works for 13 day, we can conclude that B and C work together for 2 days and C work alone for 13 - 2 = 11 days.
Work Rate(B+C) = 1/16 (work/day)
Thus, Work is done by B and C for 2 days = 2 days x 1/16 (work/day) = 1/8 work
The remaining job = 1 - 5/12 - 1/8 = (24 - 10 - 3)/24 = 11/24 work
C can finish this part of work within 11 days. Therefore, the work rate for C = 11/24 (work) x 1/11(1/day) = 1/24 (work/day)
Or C can finish one work in = 24 days
Hope this is right.
When A works for 5 days and B works for 7 days, we can conclude that A and B work together for 5 days and B works alone for 2 days. And
Work Rate(A+B) = 1/12 (work/day)
Thus, Work is done by A and B for 5 days together = 5 days x 1/12 (work/day) = 5/12 work
When B works for 7-5 = 2 days and C works for 13 day, we can conclude that B and C work together for 2 days and C work alone for 13 - 2 = 11 days.
Work Rate(B+C) = 1/16 (work/day)
Thus, Work is done by B and C for 2 days = 2 days x 1/16 (work/day) = 1/8 work
The remaining job = 1 - 5/12 - 1/8 = (24 - 10 - 3)/24 = 11/24 work
C can finish this part of work within 11 days. Therefore, the work rate for C = 11/24 (work) x 1/11(1/day) = 1/24 (work/day)
Or C can finish one work in = 24 days
Hope this is right.
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