SOLUTION: A group of workers decided to finish a work in 10 days but 5 of them could not join the team.if the crew completed the job in 12 days,then the number of members present originally

Question 705717: A group of workers decided to finish a work in 10 days but 5 of them could not join the team.if the crew completed the job in 12 days,then the number of members present originally was?
Found 2 solutions by josgarithmetic, stanbon:
Answer by josgarithmetic(39625) (Show Source): You can put this solution on YOUR website!
Let m be the original number of workers and then m-5, the number of such workers when 5 of them were not working.

Groups______rate(jobs/day)_________time(days)________Jobs
m, original____(1/10)_______________10______________1
m-5, ________(1/12)_______________12______________1

Assumption is, each worker does his task at same rate as any other worker; and rates are additive. If one worker works at r, then two workers at once work at r+r. There is 2r rate of 2 workers, 3r rate for 3 workers.

.
, the original group was 30 workers.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A group of workers decided to finish a work in 10 days but 5 of them could not join the team.if the crew completed the job in 12 days,then the number of members present originally was?
----
Let the original # of workers be "x".
That number can complete the job in 10 days.
Note: Since # of workers and # of days are indirectly related,
(# of workers) = k/(# of days)
x = k/10
k = 10x
-----
Equation:
w = (10x)/d
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If x-5 workers can complete the job in 12 days.
----
x-5 = (10x)/12
---
12x - 60 = 10x
2x = 60
x = 30 (original # of workers)
==================================
Cheers,
Stan H.
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