SOLUTION: A contract is to be completed in 56 days and 104 men were set to work, each working 8 hours a day. After 30 days, 2/5 of the work is completed. How many additional men be employed,

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: A contract is to be completed in 56 days and 104 men were set to work, each working 8 hours a day. After 30 days, 2/5 of the work is completed. How many additional men be employed,      Log On


   

Question 910701: A contract is to be completed in 56 days and 104 men were set to work, each working 8 hours a day. After 30 days, 2/5 of the work is completed. How many additional men be employed, so that the work may be completed in time if each man works 9 hours a day?
Answer by josgarithmetic(39614) About Me  (Show Source):
You can put this solution on YOUR website!
Use the data for what was done to find the one-man work rate per hour. The needed additional men would need to work for 9%2A%28DAYS%29 to do 1-2%2F5 of the job.

That is not the solution; but is only guidance on strategy for a solution.


A START FOR THE SOLUTION PROCESS:

r is the one-man rate of work, jobs per HOUR.
%28104%2Ar%29%2A%288%2A30%29=2%2F5.
Rate was 104*r, and the number of HOURS was 8%28hours%2Fday%29%2A30%28days%29=8%2A30%28hours%29.

Find r.
r=%282%2F5%29%281%2F240%29%281%2F104%29
r=2%2F%285%2A240%2A104%29
highlight_green%28r=1%2F65000%29, the one-man rate in JOBS per HOUR. That is 1 job in 65000 days, for just ONE man.

The remaining amount of job to be done will use n additional men and will require 56-30=highlight_green%2826%29 days at 9 hours per day.
... That's the idea.


FINISHING THE PROCESS:

%28104%2Bn%29%2Ar%2A%2826%2A9%29=1-2%2F5 because 2%2F5 of the job was already done.
%28104%2Bn%29%281%2F65000%29%2826%2A9%29=3%2F5
104%2Bn=%283%2F5%29%281%2F%2826%2A9%29%2965000
104%2Bn=%283%2A65000%29%2F%285%2A26%2A9%29
104%2Bn=%283%2A2500%29%2F%289%2A5%29
104%2Bn=%283%2F9%29%2825%2A100%2F5%29
104%2Bn=%281%2F3%29%28500%29
n=5000%2F3-104
theoretically, n=62%262%2F3, but realistically, the number of workers added should be highlight%2863%29.