SOLUTION: 10 men or 18 boys can do a piece of work in 15 days, in how many days will 25 men and 15 boys do the same pice of work?

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Question 828271: 10 men or 18 boys can do a piece of work in 15 days, in how many days will 25 men and 15 boys do the same pice of work?










Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
10 men or 18 boys can do a piece of work in 15 days,
in how many days will 25 men and 15 boys do the same
piece of work?
Let the answer be x days.

10 men can do 1 job in 15 days. Therefore
 1 man can do 1%2F10th of the job in 15 days.
 1 man can do 1%2F15th of 1%2F10th of the job in 1 day
Since 1%2F15th of 1%2F10th is 1%2F150th of the job,
 1 man can do 1%2F150th of the job in 1 day.
25 men can do 25%2F150ths of the job in 1 day.
Reduce the fraction:
25 men can do 1%2F6th of the job in 1 day.
25 men can do x%2F6ths of the job in x days. 

18 boys can do 1 job in 15 days, so
 1 boy can do 1%2F18th of the job in 15 days.
 1 boy can do 1%2F15th of 1%2F18th of the job in 1 day
Since 1%2F15th of 1%2F18th is 1%2F270th of the job,
 1 boy can do 1%2F270th of the job in 1 day.
15 boys can do 15%2F270ths of the job in 1 day.
Reduce the fraction:
15 boys can do 1%2F18th of the job in 1 day.
15 boys can do x%2F18ths of the job in x days. 

The equation comes from:

%22%22%2B%22%22  %22%22=%22%22 %28matrix%283%2C1%2Cone%2Cwhole%2Cjob%29%29

x%2F6%22%22%2B%22%22x%2F18 %22%22=%22%22 1

Multiply through by LCD of 18

3x + x = 18
    4x = 18
     x = 18%2F4
     x = 9%2F2
     x = 4%261%2F2 days.

Edwin