SOLUTION: It takes 5 boys or 8 girls complete a job in 26 days. How many days would it take 4 boys and 5 girls to complete the same job?

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Question 221771: It takes 5 boys or 8 girls complete a job in 26 days. How many days would it take 4 boys and 5 girls to complete the same job?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
This problem is about the rates at which
boys and girls do a certain "job".
given:
The rate for 5 boys is 1 job/26 days.
Each boy can do 1/5 of a job in 26 days because
.2%2F26+%2B+.2%2F26+%2B+.2%2F26+%2B+.2%2F26+%2B+.2%2F26+=+1%2F26
%28.2+%2B+.2+%2B+.2+%2B+.2+%2B+.2%29%2F26+=+1%2F26
How long does it take a boy to do 1 job?
%28%281%2F5%29%2F26%29%2A%285%2F5%29+=+1%2F130
1 boy can do 1 job in 130 days
likewise,
The rate for 8 girls is 1 job/26 days
Each girl can do 1/8 job in 26 days
How long does it take a girl to do 1 job?
%28%281%2F8%29%2F26%29%2A%288%2F8%29+=+1%2F208
A girl can do 1 job in 208 days
I can add up the rates for 4 boys and 5 girls
to get their rate working together
Let d = number of days for 4 boys and 5 girls
to complete job

4%2A%281%2F130%29+%2B+5%2A%281%2F208%29+=+1%2Fd
Multiply both sides by 130%2A208%2Ad
4%2A208%2Ad+%2B+5%2A130%2Ad+=+130%2A208
832d+%2B+650d+=+27040
1482d+=+27040
d+=+18.246 days
check answer
4%2A%281%2F130%29+%2B+5%2A%281%2F208%29+=+1%2Fd
.0308+%2B+.0240+=+1%2F18.246
.0548+=+.0548
OK
check for 5 boys
5%2A%281%2F130%29+=+1%2F26
.0385+=+.0385
check for 8 girls
8%2A%281%2F208%29+=+1%2F26
.0385+=+.0385
OK