SOLUTION: A project can be done by 8 girls in 5 days. 5 boys can do the same project in 6 days. How long will it take for 3 boys and 6 girls to do the job?

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Question 483521: A project can be done by 8 girls in 5 days. 5 boys can do the same project in 6 days. How long will it take for 3 boys and 6 girls to do the job?
Answer by emargo19(101) About Me  (Show Source):
You can put this solution on YOUR website!
8 girls can do it in 5 days, so 1 girl can do it in 40 days.
So each girl's rate is 1 job per 40 days or 1%2F40 job/day
5 boys can do it in 6 days, so 1 boy can do it in 30 days.
So each boy's rate is 1 job per 30 days, or 1%2F30 job/day.
3 boy's combined rate is 3%2F30 or 1%2F10 jobs/day
6 girl's combined rate is 6%2F40 or 3%2F20 jobs/day.
Let x be the number of days for 3 boys and 6 girls to do the job.
Then in those x days, the boys do 1%2F10x of the job and the girls
do 3%2F20x of the job. That must add to 1 job so the equation is
1%2F10x + 3%2F20x = 1
Multiply through by 20
2x + 3x = 20
5x = 20
x = 4 days