SOLUTION: If 5 adults and 2 children work together, a job can be done in a day. If only 2 adults work, then 6 children must work in order to complete the job in a day. The number of days tha

Algebra ->  Rate-of-work-word-problems -> SOLUTION: If 5 adults and 2 children work together, a job can be done in a day. If only 2 adults work, then 6 children must work in order to complete the job in a day. The number of days tha      Log On


   

Question 276491: If 5 adults and 2 children work together, a job can be done in a day. If only 2 adults work, then 6 children must work in order to complete the job in a day. The number of days that it takes for a child to do the job alone is:
a 9 b 25/3 c 26/3 d 8 e none of above
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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If 5 adults and 2 children work together, a job can be done in a day.
If only 2 adults work, then 6 children must work in order to complete the job in a day.
The number of days that it takes for a child to do the job alone is:
:
Let a = time required when adult does the job alone
let c = time required when a child does it
:
Let the completed job = 1
:
5%2Fa + 2%2Fc = 1
and
2%2Fa + 6%2Fc = 1
:
Therefore:
2%2Fa + 6%2Fc = 5%2Fa + 2%2Fc
6%2Fc - 2%2Fc = 5%2Fa - 2%2Fa
4%2Fc = 3%2Fa
Cross multiply
4a = 3c
a = 3%2F4c
a = .75c
:
Using the 1st equation replace a with .75c, find c
5%2F%28.75c%29 + 2%2Fc = 1
Multiply equation by 3c, results
4(5) + 3(2) = 3c
20 + 6 = 3c
c = 26%2F3 days for a child alone