The SAT isn’t the only
nerdy thing I like.

I’m absolutely swamped with work at school. Just completely swamped. Which is why I’m sitting here trying to come up with a good weekend challenge, of course. I like procrastination almost as much as I like frozen cheese ravioli. And I like frozen ravioli a lot.

Everyone hates work problems like the one I’m about to throw at you. Even I kinda hate them, honestly. You probably wouldn’t see this on the SAT (where work problems are rare and basically limited to the easier special case of distance = rate × time problems), but of course, you’d never see most of the stuff I throw at you as Weekend Challenges on the SAT. These Weekend Challenges are like cross-training. You’re working the same muscles, but doing slightly different exercises.

Enough rambling. You know the drill by now. First correct response in the comments wins everyone else’s undying adoration. Here’s your challenge:

It would take Jerry 13 hours to paint the fence in his yard by himself. If his friend Susannah helped, it would take the two of them 6 hours to paint the fence. If their friend Lori also helped, the three could paint the whole fence in just 2 hours. How fast could Lori paint the fence by herself?

Good luck, folks. I’ll post the solution Monday (or maybe Tuesday).

UPDATE: Congrats to gottagetmealife for getting the right answer first, and thanks to JD for saving me the trouble of having to write up my own explanation. See his comment below to see how simple this question could have been. I’ll only add (to say implicitly what JD implied) that you don’t need to know at all how fast Susannah is. She’s just in there to mess with you. I hope you can find it in your hearts to forgive me for that. 🙂

Comments (6)

1/13+1/s=1/6 (s is time it would take Susannah to do the job by herself).  Solve this for s.  s=78/7

then 1/13+1/(78/7)+1/L=1/2, so L=3 .  Takes Lori 3 hrs to do the job by herself.

C’mon guys, too much algebra! This problem is much simpler…

Jerry and Susannah can paint a whole fence in 6 hours, so in 2 hours they can paint 1/3 of a fence.

But with the help of Lori, the whole fence is painted in 2 hours. Therefore Lori must be able to paint 2/3 of the fence in 2 hours.

If Lori can paint 2/3 of a fence in 2 hours, then obviously she can paint the whole fence in 3 hours.


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