SOLUTION: three man can finish a painting job in 8 days. This job can be finished by 5 women in 6 days and by 8 boys in 10 days. how long will it take 1 man 2 women and 3 boys working togeth

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Question 140075: three man can finish a painting job in 8 days. This job can be finished by 5 women in 6 days and by 8 boys in 10 days. how long will it take 1 man 2 women and 3 boys working together?
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Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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three man can finish a painting job in 8 days. This job can be finished by 5 women in 6 days and by 8 boys in 10 days. how long will it take 1 man 2 women and 3 boys working together?
:
Approach this using; man-days, girl-days, boy-days:
;
The job requires:
3 * 8 = 24 man-days
or
5 * 6 = 30 girl-days
or
8 * 10 = 80 boy-days
:
Let t = required time for 1 man 2 girls and 3 boys to complete the job
Let the completed job = 1
:
1t%2F24 + 2t%2F30 + 3t%2F80 = 1
:
Multiply equation by 240 to get rid of the denominator:
10(1t) + 8(2t) + 3(3t) = 240
:
10t + 16t + 9t = 240
:
35t = 240
t = 240%2F35
t = 6.857 days (6 days 20 hrs 34 min) for 1 man, 2 girls, and 3 boys to do the job
:
:
Check solution:
6.857/24 + 2(6.857)/30 + 3(6.857)/80
6.857/24 + 13.714/30 + 20.571/80
.286 + .457 + .257 = 1;