SOLUTION: a man can do a job in 8 hours, a boy can do the same job in 12 hours and a girl can do it in 16 hours. how long will it take them to do the job if the man and the boy work together

Algebra ->  Rate-of-work-word-problems -> SOLUTION: a man can do a job in 8 hours, a boy can do the same job in 12 hours and a girl can do it in 16 hours. how long will it take them to do the job if the man and the boy work together      Log On


   

Question 854084: a man can do a job in 8 hours, a boy can do the same job in 12 hours and a girl can do it in 16 hours. how long will it take them to do the job if the man and the boy work together for one hour and then the boy and the girl finish the job
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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a man can do a job in 8 hours, a boy can do the same job in 12 hours and a girl can do it in 16 hours.
how long will it take them to do the job if the man and the boy work together for one hour and then the boy and the girl finish the job.
:
Let t = time worked by the boy
then
(t-1) = time worked by the girl
:
The completed job = 1
Each will do a fraction of the job, the three fractions add up to 1
:
The man worked 1 hr therefore
1%2F8 + t%2F12 + %28%28t-1%29%29%2F16 = 1
multiply by the LCM, 96; cancel the denominators
12 + 8t + 6(t-1) = 96
8t + 6t - 6 = 96 - 12
14t = 84 + 6
14t = 90
t = 90/14
t = 6.43 hrs worked by the boy who worked the whole time to complete the job