##### May 28, 2018

**RAY:** 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 to 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?

**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?