Math Question - Rates

larryphang (69) in math • 7 years ago

5 men are hired to complete a job. If one more man is hired, the job can be completed 8 days earlier. Assuming all man work at the same rate, how many more men should be hired so that the job can be completed 28 days earlier?

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7 years ago by larryphang (69)

$6.38

14 votes

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sabrin514 (45) · 7 years ago

wd= work days per person

6(wd-8) = 5days
6 wd - 48 = 5days
1 wd = 48

5 x 48 wd = 240 total days to complete with 5

(m+5)(48-28)= 240
(m+5)20= 240
20m+100=240
20m=140
m = 7

7 is the number of extra men needed, but the total number working is 12.

$0.48

2 votes

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jrvacation (68) · 7 years ago

This looks correct

$0.00

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larryphang (69) · 7 years ago

👏🏻👏🏻👏🏻👏🏻
You are right

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culgin (71) · 7 years ago

Oops.. didn't see this answer before replying. Seems like I am too slow to answer :)

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culgin (71) · 7 years ago (edited)

Total number of mandays required = W
W/5 - W/6 = 8
Multiply 30 on both sides:
6W - 5W = 240
W = 240
Total additional number of workers to hire to complete work 28 days earlier = N
240/5 - 240/(5+N) = 28
48 - 240/(5+N) = 28
48(5+N) - 240 = 28(5+N)
240 + 48N -240 = 140 + 28N
20N = 140
N = 7

But in real life, we all know that usually the total number of days will not reduce even if more people "work" on it. There will just be more people using "eye power" :)