Painting Car Talk Plaza
RAY: Dougie's not going to like this answer at all.
Let T represent the amount of the place that Tommy can paint in a day, let R represent the amount I could paint in a day, and D will represent the amount Dougie could paint in a day.
So, we come up with the following little equation. T plus R equals one over ten. We'll change that one over ten to three over thirty. You'll find why in a second.
TOM: Where did you get T plus R equals one over ten?
RAY: That's the amount of work that you could do in one day plus the amount of work that I could do in one day. It equals one tenth, because we could together paint Car Talk Plaza in ten days.
RAY: By the same token D plus R; that is, Dougie and I working together, could paint Car Talk Plaza in 15 days.
TOM: So D plus R equals one over 15.
RAY: Right. Now, take the second equation and change all the signs so it's minus D, minus R equals minus one fifteenth.
TOM: Then you add that to the first equation, right?
RAY: Right. And, you'll notice, when you do that, the R's fall out, and you get the following equation: T minus D equals one over thirty.
But here's what's interesting. I said T plus D equals one thirtieth. We have a problem here.
TOM: It looks like D equals zero.
RAY: So Doug contributes nothing. What else is new? Who's our winner, Tommy?
TOM: The winner is John Boyer from Manhattan, Kansas. Congratulations, John!
[ Car Talk Puzzler ]