Math Is Fun Forum

ahgua

Member

Registered: 2005-08-24

Posts: 25

Variations

I got stumbled by a question on variations. So pls help me!!!

5 men are hired to complete a certain job. If one more man were hired, the job can be completed 8 days earlier. Given that the no. of days required to complete the job is inversely proportional to the mo. of the men hired, find how many additional men must be hired in order for the job to be completed 28 days earlier.

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Life is a passing dream, but the death that follows is eternal...

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,423

Re: Variations

Lets assume the job can be completed by 5 men in 'x' days.
Therefore, the number of mandays required is 5x.
If one more man is hired, the total number of men = 6 and the number of days required = x-8. Therefore, the total number of mandays = 6(x-8)
Equating the two,
5x = 6(x-8)
5x = 6x - 48
-x = -48 or x = 48.
Therefore, the number of mandays required for the work is 5x48 = 240.
If y men moreare employed for completion of the work in 28 days earlier,
number of men = 5+y, number of days = 48-28=20,
the number of mandays = (5+y)20
but, we already know that the number of mandays required for the work is 240,
therefore,
(5+y)20=240, 5+y=240/20 => 5+y=12, y=7
Therefore, 7 more men would be required.

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

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mikau

Member

Registered: 2005-08-22

Posts: 1,504

Re: Variations

I love the more abstract rate problems! :-D

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A logarithm is just a misspelled algorithm.

wcy

Member

Registered: 2005-08-04

Posts: 117

Re: Variations

if y is inversely proportional to x then y=k/x, where k is a constant