|
Question 936590: The number of hours required to do a painting job is represented by the function f(x)=2x , where f(x) gives the number of hours and x is the number of painters doing the job. How much time will {4, 10, 14, 16, 18} workers take to do the job?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the equation is f(x) = 2x
based on this equation:
4 workers will take 8 hours.
10 workers will take 20 hours.
14 workers will take 28 hours.
16 workers will take 32 hours.
18 workers will take 36 hours.
that's you solution, and you can stop here if you want to.
otherwise, read on.
this doesn't make sense, since you would think that more workers would take less time to do the same job.
if you assume that f(x) is equal to the overall rate that they work, then it makes more sense.
the formula for work is:
r * p * t = q
r is the rate of one person.
p is the number of persons working at the same rate.
t is the amount of time to do the job.
q is the quantity of work.
in this problem, we would translate the numbers as follows:
2 = rate of one worker.
x = number of workers.
t is what we want to find.
q is 1 job.
the formula of r * p * t = q becomes:
2 * x * t = 1
solve for t in this equation to get:
t = 1 / (2 * x)
if x = 1, then the job is finished in 1/2 hours.
if x = 4, then the job is finished in 1/8 of an hour.
if x = 10, the job is finished in 1/20 of an hour.
etc.
bottom line is more workers to do the same job results in less time to do the job assuming they all work at the same rate per worker.
in real life, there is an optimal number of workers after which the efficiency drops off and the average rate per worker decreases.
|
|
|
| |
