A B and C can finish a job in 6 days If B and C work together the job will take 9 days if A and C work together the job will take 8 days In how many days can each man working alone do the job?

Answer 1

Define the time (in days) taken by each person as: TA, TB and TC. In one day, A, B and C can respectively complete the following proportions of the work: 1/TA, 1/TB and 1/TC So together, they complete 1/TA + 1/TB + 1/TC of the work. It follows that they take 1 / [1/TA + 1/TB + 1/TC] days to complete the job together. So we can write * 6 = 1 / [1/TA + 1/TB + 1/TC] And by similar arguments: * 9 = 1 / [1/TB + 1/TC] * 8 = 1 / [1/TA + 1/TC] Solve the three equations simultaneously: * 1/6 = 1/TA + 1/TB + 1/TC * 1/9 = 1/TB + 1/TC subtracting yields 1/6 - 1/9 = 1/TA 1/TA = 1/18 * 1/9 = 1/TB + 1/TC * 1/8 = 1/18 + 1/TC subtracting yields 1/8 - 1/9 = 1/18 - 1/TB 1/TB = 1/9 - 1/8 + 1/18 = 3/72 = 1/24 and finally 1/TC = 1/8 - 1/18 = 5/72 Thus: TA = 18, TB = 24, TC =72/5.