SOLUTION: 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 m

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.

RELATED QUESTIONS
The cost of renting a jet-ski at a lake is represented by the equation {{{f(x)=25+100}}}... (answered by josmiceli)

Find the rule of the linear function f that gives the number of hours in x days. (answered by richard1234)

Wendy is looking over some data regarding the strength, measured in Pascals (Pa), of some (answered by Alan3354)

The total cost of a cab ride can be represented by the functions f(x) = 3x + 2.5, where x (answered by josgarithmetic,Boreal)

The function f is given by f(x)=x^3+2x^2+ax-8 where a is constant.when f(x) is divided... (answered by ikleyn,MathLover1,MathTherapy)

What is the greatest zero of the function f, where f(x) = x^3 - 2x -... (answered by Edwin McCravy)

Determine the difference quotient f(x+h)-f(x)/h (where h cannot =0) for the function... (answered by Alan3354)

Let f be the function defined by {{{f(x)=2x^4+5}}}. Find f(a+h),... (answered by jim_thompson5910)

Appreciate if you could explain a step by step in detail how to get the answer (C).... (answered by ikleyn,math_tutor2020,greenestamps)