SOLUTION: Question 1)5 men are hired to complete a job.If one more man is hired, the job can be completed 8 days earlier.Assuming that all the men work at the same rate, How many more men sh

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Question 840925: Question 1)5 men are hired to complete a job.If one more man is hired, the job can be completed 8 days earlier.Assuming that all the men work at the same rate, How many more men should be hired so that the job can be completed 28 days earlier?
Question 2)It is given that z is directly proportional to x2 and inversely proportional to √y
i)Write down an equation connecting x, y and z
ii) if z = 16 when x = 2 and y = 9 ,find the value of z when x =5 and y =4
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
5 men are hired to complete a job.
If one more man is hired, the job can be completed 8 days earlier.
:
Let d = original number of days to complete the job
5d = no. of man-days required
:
when one more man is hired
6(d-8) = no. of man-days with six men
therefore
6(d-8) = 5d
6d - 48 = 5d
6d - 5d = 48
d = 48 days when 5 men are hired
5*48 = 240 man-days required to complete the job (same as 6*40)
:
Assuming that all the men work at the same rate, How many more men should be hired so that the job can be completed 28 days earlier?
Let m = no. of additional men required
(m+5)(48-28) = 240
(m+5)*20 = 240
20m + 100 = 240
20m = 240 - 100
m = 140/20
m = 7 more men for a total of 12,
:
Check by finding the man-hrs 12*20 = 240 man-hrs completes the job
:
:
It is given that z is directly proportional to x^2 and inversely proportional to
i)Write down an equation connecting x, y and z

:
ii) if z = 16 when x = 2 and y = 9
let k = the constant of variation, and write the equation:

find k
= = 3(16) = 4k
4k = 48
k = 48/4
k = 12
write the equation now as
find the value of z when x =5 and y =4

z = 150
:
Any questions to ankor@att.net