SOLUTION: A contractor agrees to lay a road 3000m long in 30 days. 50 men are employed and they work for 8 hours per day. After 20 working days, he finds that only 1200m of the road is compl

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Question 1117273: A contractor agrees to lay a road 3000m long in 30 days. 50 men are employed and they work for 8 hours per day. After 20 working days, he finds that only 1200m of the road is completed. How many more men does he need to employ in order to finish the project on time if each man now works 10 hours a day?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39615) About Me  (Show Source):
You can put this solution on YOUR website!
First 20 days
50r%2A8%2A20=1200
r=3%2F20

Last 10 days
%2850%2Bn%29%283%2F20%29%2A10%2A10=1800
%28n%2B50%29%283%2F20%29=18

n%2B50=18%2820%2F3%29=6%2A20=120
n=120-50
highlight_green%28n=70%29moreworkers

Answer by ikleyn(52767) About Me  (Show Source):
You can put this solution on YOUR website!
.
50 men working 8 hours per day 20 working days, spent  50*8*20 = 8000 men-hours.


Let n be the number of men to employ additionally.


Then the team will count (50+n) workers, that are to complete the remaining 1800 m working 10 hours per day during remaining 10 days.


The equation for the constant rate of work is


1200%2F8000 = 1800%2F%28%2850%2Bn%29%2A10%2A10%29.


From this proportion,   50+n = %281800%2A8000%29%2F%281200%2A10%2A10%29 = 120.


Hence,  120 - 50 = 70 workers should be employed additionally to complete the work under given conditions.

Solved.

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