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# Direct

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619
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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?

May 26, 2015

#3
+95361
+10

ok we might as well all answer this question!

This is how I was trained to do it

$$\\T\alpha \frac{L}{N} \\\\ T=k* \frac{L}{N}\qquad but\\\\ 5=k* \frac{200}{3}\qquad so\\\\ k=\frac{3}{40}\qquad so\\\\ T=\frac{3L}{40N}\\\\ When N=5 and L=500\\\\ T=\frac{3*500}{40*5}\\\\ T=7.5 \;\;hours$$

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May 26, 2015

#1
+27377
+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

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May 26, 2015
#2
+94607
+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.

May 26, 2015
#3
+95361
+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
#4
+94607
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Which can we do faster.......paint that fence or answer this question?????

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

May 26, 2015
#5
+72
+5

Depends on how much  You can take 60 seconds on writing this while 70 painters paint a small fence 3*3 fence

May 26, 2015
#6
+72
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Hello CPhill

May 26, 2015