SOLUTION: 25 men can do a project in 20 days . 15 men leave the project after working for some timeand the remaining project is completed in the next 37 1/2 days . After how many days did th

Algebra ->  Rate-of-work-word-problems -> SOLUTION: 25 men can do a project in 20 days . 15 men leave the project after working for some timeand the remaining project is completed in the next 37 1/2 days . After how many days did th      Log On


   



Question 683824: 25 men can do a project in 20 days . 15 men leave the project after working for some timeand the remaining project is completed in the next 37 1/2 days . After how many days did those men leave ?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +n+ = number of days after starting when 15 men left
The 25 men work at a rate of ( 1 project ) / ( 20 days ), or +1%2F20+
What fraction of the project did they complete in +n+ days?
+%281%2F20%29%2An+=+n%2F20+ of the project
That means that the fraction of the project left to be done is
+1+-+n%2F20++
-------------
Now there are +20+-+15+=+5+ men left to finish the project
If 25 men work at a rate of +1%2F20+, then 5 men will be
5 times slower, or a rate of +%281%2F5%29%2A%281%2F20%29+=+1%2F100+
Now I can say
+1%2F100+=+%28+1+-+n%2F20+%29+%2F+37.5+
+.375+=+1+-+n%2F20+
Multiply both sides by +20+
+7.5+=+20+-+n+
+n+=+20+-+7.5+
+n+=+12.5+
The 15 men left after 12.5 days
check answer:
The original 25 men finished
+n%2F20+=+12.5%2F20+
+.625+ as a fraction of the project
There was +1+-+.625+=+.375+ left to do
The remaining 5 men work at a rate of +1%2F100+
+1%2F100+=+.375+%2F+37.5+
+37.5%2F100+=+.375+
OK