Proportion and chain rule

[maihuna]

A contract is to be completed in 46 days and 117 men were set to work, each working 8 hrs a day. After 33 days 4/7 of the work is completed. How many additional men may be employed so that the work may be completed in time, each men now working 9 hrs a day?

a.46
b.57
c.64
d.75
e.81

[lilu]

A contract is to be completed in 46 days and 117 men were set to work, each working 8 hrs a day. After 33 days 4/7 of the work is completed. How many additional men may be employed so that the work may be completed in time, each men now working 8 hrs a day?

a.46
b.57
c.64
d.75
e.81

Are you sure the number of hours a day does not change for the 3/7 of the project that is left to be done?

[maihuna]

sorry met it is 9 hrs, edited the post

[lilu]

A contract is to be completed in 46 days and 117 men were set to work, each working 8 hrs a day. After 33 days 4/7 of the work is completed. How many additional men may be employed so that the work may be completed in time, each men now working 8 hrs a day?

a.46
b.57
c.64
d.75
e.81

i get 105 workers and that's not one of the options.
117men*8hrs*33days=4/7 of a job
30888hrs=4/7 of job
30888/ 4/7 = x hrs / 3/7
x=23166 hrs
#of workers*13 days*8hours=23166
#of workers=222.75~223
223-117=105..... and that's not one of the answer choices.... :roll:

[lilu]

OH!
That's what I thought!
Then--->
117men*8hrs*33days=4/7 of a job
30888hrs=4/7 of job
30888/ 4/7 = x hrs / 3/7
x=23166 hrs
#of workers*13 days*9hours=23166
# of workers=198
AND 198-117=81

I am not I'd be able to do this one in under two minutes b/c of all the calculations....

[dumb.doofus]

OH!
That's what I thought!
Then--->
117men*8hrs*33days=4/7 of a job
30888hrs=4/7 of job
30888/ 4/7 = x hrs / 3/7
x=23166 hrs
#of workers*13 days*9hours=23166
# of workers=198
AND 198-117=81

I am not I'd be able to do this one in under two minutes b/c of all the calculations....

I think you can do it in two mins or less.. if you don't calculate so much.. so here is what I suggest:

Job done in 33 days by 117 men = 117*33*8 ------ (1)
This is 4/7 of the total job

Job done in 13 days by y men = y*13*9 --------- (2)
This is 3/7 of the total job..

So essentially the ratio of (1) and (2) should be equal to 4/3

i.e.

(117*33*8)/(y*13*9) = 4/3

13*9 = 117.. so that easily cancels out.. and actually its pretty simple calculation..

x = 198..

So extra men required = 81

[lilu]

Great approach,Smart.Guy!!!

[maihuna]

dumb, its an question of setting up proportion, its too late here, i will soon post my version of ans..

[dtweah]

A contract is to be completed in 46 days and 117 men were set to work, each working 8 hrs a day. After 33 days 4/7 of the work is completed. How many additional men may be employed so that the work may be completed in time, each men now working 8 hrs a day?

a.46
b.57
c.64
d.75
e.81

i get 105 workers and that's not one of the options.
117men*8hrs*33days=4/7 of a job
30888hrs=4/7 of job
30888/ 4/7 = x hrs / 3/7
x=23166 hrs
#of workers*13 days*8hours=23166
#of workers=222.75~223
223-117=105.....

If abc is proportional to d, and efg is proportional to h we set up the proportion as follows. Find the proportionality constant k in the first proportion. Use in the second to solve for variable of interest.

abc=kd

k= abc/d.

In the problem if e is the number of men working then

Efg=k h

E= k x h/ f x g

E= ((117 x 8 x 33)/4/7 x 3/7 ) / 9 x 13.

E=198
198-117=81.

Warning: in problems involving big numbers, try to avoid multiplying the numbers. Leaving them as is can be helpful especially if you will have to break them up again.