Tom, Ray and Doug Paint Car Talk Plaza

The Puzzler

RAY: The question is how long would it take each of us working alone to paint Car Talk Plaza? 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 Donna Ballinger from Seattle, Washington.

[ Car Talk Puzzler ]

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