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

[cory]

How long will it take to paint a fence twice as long if they work together?

It took me over 10 minutes to get what I think is the right answer. I'm not good with math though I think it is hugely fascinating.

I don't usually go for problems like this but for some reason this one hooked me.

How to Solve Any Problem Using Just Common Sense (Published 2021)

Contemplating Fermi problems keeps me curious about the world and how things relate to one another.

www.nytimes.com

 

[lxskllr]

12 hours, cause John hates painting fences, and he'll be off clearing hedge rows or something while Sarah paints the fence.

 

[flushcut]

Yep, Sarah is by far more profitable.

 

[Jonny]

I think read something about it being easy if you offer a passerby a dead rat with a string to swing it with.

 

[cory]

How long would it take Tom Sawyer?

 

[flushcut]

Was (I've ran out of vocabulary) Jim helping?

Interesting text edit.

 

[cory]

Yes Jim helped but it turns out John is hot for sarah so did his rate increase or decrease?

 

[flushcut]

It depends what Sarah is wearing? If she is wearing next to nothing and Sarah is warm for his form the fence may never get finished. If she is dressed like a nun the fence may get painted in record time.

 

[cory]

Let's assume she is wearing a painter's thong.

 

[lxskllr]

I think John's starting to get more interested in painting fences.

 

[cory]

It has it's perks

 

[Mellow]

8 hours

 

[cory]

How long did it take youse to figure

 

[treesmith]

Average their speed and double.

 

[cory]

How do you figure their average speed?

 

[treesmith]

6 + 12 = 18.....18/2 = 9 hours...Divided by two, if they were painting together....yields 4.5 hours for original fence....times 2 (for additional fence)...gives us 9 hours for both fences.

 

[flushcut]

12 hours. Sarah will have it painted while John is drinking beer tending to the smoke house listening to the game and hanging with his buds.

 

[cory]

6 + 12 = 18.....18/2 = 9 hours (to paint original fence).... x 2 (fence twice as long) = 18 hours.

I believe Mellow has provided the correct answer.

I believe it would take them 4 hours together to paint the first fence

 

[No_Bivy]

4 hours

1/6 + 1/12 = 1/x
3/12= 1/x
x=4

 

[lxskllr]

Going with the spirit of the original article(how to estimate, and whether or not an answer seems sane), the longest it can take to paint the fence is 12hr, if the fastest painter(Sarah) does it all herself. Any answer will have to be <12hr. Mellow's seems right, but I haven't checked the math.

edit:
added words

 

[stig]

Somehow a rat and a piece of string to swing it with should figure in.

 

[BlackSmith]

Pix of Sarah aren’t loading for me.

 

[cory]

 

[cory]

Not only is she a hella painter, she's handy with a paddle too.

 

[treesmith]

If it would take Sarah 12 hours to paint both fences, and John 24 hours to paint both fences, how the blazes are they gonna paint BOTH in 4 hours?