Problema Solution
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. How many days will it take each man to do the job alone?
Answer provided by our tutors
Let
a = the number of days that a needs to finish the job
1/a per day = the rate of a
b = the number of days that b needs to finish the job
1/b per day = the rate of b
c = the number of days that a needs to finish the job
1/c per day = the rate of c
1/a + 1/b + 1/c = 1/6
1/b + 1/c = 1/9
1/a + 1/c = 1/8
by solving we find
1/a = 1/6 - 1/9
1/a = (3 - 2)/18
1/a = 1/18
a = 18 days
1/c = 1/8 - 1/a
1/c = 1/8 - 1/18
1/c = (9 - 4)/72
1/c = 5/72
c = 72/5
c = 14.4 days
1/b = 1/9 - 1/c
1/b = 1/9 - 5/72
1/b = (8 - 5)/72
1/b = 3/72
1/b = 1/24
b = 24 days
A needs 18 days to finish the job, b needs 24 days while c needs 14.4 days to finish the job.