the time needed to paint a fence varies directly with the length if the fence and indirectly with the number of painters. if it takes 5 hours to paint 200 feet of fence with 3 painters, how long will it take 5 painters to paint 500 feet of fence?

Guest May 26, 2015

#3**+10 **

ok we might as well all answer this question!

This is how I was trained to do it

$$\\T\alpha \frac{L}{N} \\\\

T=k* \frac{L}{N}\qquad but\\\\

5=k* \frac{200}{3}\qquad so\\\\

k=\frac{3}{40}\qquad so\\\\

T=\frac{3L}{40N}\\\\

$When N=5 and L=500$\\\\

T=\frac{3*500}{40*5}\\\\

T=7.5 \;\;hours$$

Melody
May 26, 2015

#1**+10 **

The rate at which fence painting is done is 200/(3*5) feet per painter-hour.

In order to paint 500 feet we need 500*3*5/200 painter-hours

With 5 painters the time taken is 500*3*5/(200*5) hours = 7.5 hours

.

Alan
May 26, 2015

#2**+10 **

If 3 painters paint 200 ft of fence in 5 hours, in 1 hour, they must paint 40 ft.......so each painter paints 40/3 ft per hour.

Then, 5 painters can paint 200/3 ft every hr........so........500/ (200/3) = 1500/200 = 7.5 hrs.

CPhill
May 26, 2015

#3**+10 **

Best Answer

ok we might as well all answer this question!

This is how I was trained to do it

$$\\T\alpha \frac{L}{N} \\\\

T=k* \frac{L}{N}\qquad but\\\\

5=k* \frac{200}{3}\qquad so\\\\

k=\frac{3}{40}\qquad so\\\\

T=\frac{3L}{40N}\\\\

$When N=5 and L=500$\\\\

T=\frac{3*500}{40*5}\\\\

T=7.5 \;\;hours$$

Melody
May 26, 2015

#4**0 **

Which can* we* do faster.......paint that fence or answer this question?????

{ I say its a toss up..... }

CPhill
May 26, 2015