Sarah takes 6 hours to paint a fence and John takes 12 hours to paint the same fence.

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  • #27
Gonna take 8 hours to paint the double length fence working together
 
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  • #33
Mellow and I say 8hrs.

Ok, let's say they started at the same time. After 6 hours, she would have the full length of the first fence painted, and since he paints half as fast, he would have half that distance painted which is equal to half the length of the first fence.

So after 6 hours they have 3/4 of the double length fence painted ( the full first fence length plus half the full first length = 3/4 of the double fence length)

Therefore it will take them 2 more hours to paint the last quarter of the fence length because each quarter of the fence took them 2 hours.
 
The fence length is X.
Sarah can paint the fence in 6hr
John can paint a fence in 12hr.
The fence in question is twice as long, or 2X.

Sarah's speed is X/6hr
John's speed is X/12hr
Collectively they're painting X/6hr+X/12hr per hour which equals X/4hr

Thus:
2x=X/4hr
4hr*2x=X
8hrX=X
8hr
 
My initial answer is 4hrs, but I rethunk it, and still got 4 hrs

However long she works, he does half the work. If she works 4 hrs, he will have worked 4 hrs too, but completed half the work (2 of her hours) which completes 6 of her hours in total.
 
I didn't read the article (used up my free reads and not subscribing), but my assumption from reading here was the fence in question is twice as long.

Given the assumptions listed at the beginning of my post, the answer is 8hr for the pair to paint a fence 2x as long.
 
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  • #41
First sentence of the OP
 
It takes Sarah 6 hours to paint the first fence while John is half way thru the second fence. Sara is twice as fast as John.
6+6=12 man hours so it counts as 6 actual hours with one half of the second fence remaining. Sarah will have half of that fence finished before John finishes half of the remaining quarter. So +3 combined hours. 9 hours total so far with one remaining eigth of a fence left. So Sarah put in the last 2 hours for 11 hours and what ever piss poor effort John put in at the end.
11.5xxxx hours how did I do?
And all this is assuming they are working together. If not 18 hours.
 
I think a simplified equation would be 12/1.5. 12hr is the upper bound of time(Sarah paints it all herself), add in John's 50% effort(optimistic imo :^P ), you get 8hr.
 
lumberjack said:
I didn't read the article (used up my free reads and not subscribing), but my assumption from reading here was the fence in question is twice as long.

Given the assumptions listed at the beginning of my post, the answer is 8hr for the pair to paint a fence 2x as long.
Click to expand...
I never got free reads, but they gave me a few seconds to take a screen shot of the article.
 
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