Puzzler of the week

[Scott MacLean]

This week's puzzler:

The other day, one of the neighbors and I were having a little conversation.

He was asking about my radio show. It took him a while, but he finally got around to asking how much preparation we do in advance of every show. And, I had to tell him, we don't do much preparation at all.

He said, "Oh, in that case, every week, you're pretty much wingin' it."

And, I said, "Well, not exactly."

Which, conveniently, leads me to this week's puzzler question. Where does the term "wingin' it" come from and what does it mean?

Last week's puzzler:

Tommy, Dougie and I are sitting around the office one day at Car Talk Plaza. We were noticing how dingy the place looked. We'd been there 15 years, and the place had never been painted. So, we decided to paint Car Talk Plaza.

We didn't know which team of us was going do it, so we sat down and decided to do a little math. We determined that Tommy and I together could paint the entire Car Talk plaza in 10 days. After all, we had a lot of painting experience as kids, having painted Dad's car a couple of times with brushes.

Dougie and I could do it in 15 days. And, if Doug and Tom worked together, they could do it in 30 days.

The question is how long would it take each of us, painting by ourselves, to paint
the whole of Car Talk Plaza?

Last week's puzzler answer:

Let T represent the amount of the place that Tommy can paint in a day, let R represent the amount Ray 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.

Where did I get T plus R equals one over ten?

That's the amount of work that Tommy could do in one day plus the amount of work that Ray could do in one day. It equals one tenth, because we could together paint Car Talk Plaza in ten days.

By the same token D plus R; that is, Dougie and Ray working together, could paint Car Talk Plaza in 15 days.

So D plus R equals one over 15.

Right. Now, take the second equation and change all the signs so it's minus D, minus R equals minus one fifteenth. Then you add that to the first equation. 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. It looks like D equals zero. So Doug contributes nothing. What else is new?