# Doing the Math on the Ever-Slowing Drive

RAY: What you wind up with is a series of numbers. If you start counting from your destination of one hour, plus a half an hour, plus a third of an hour, plus a fourth, plus a fifth, plus a sixth, and when you're driving at 60 miles an hour, that mile takes you one sixtieth of an hour obviously which is a minute.

I got the answer by adding up one plus a half, plus a third, and so on. I converted them all to decimals.

There's no discrete answer, the best you can get is an approximation. Here's how you get it: you have 75 terms. You're going to look up the natural log of 75, which happens to be 4.317, and you're going to add it to something called Euler's constant.

Euler was a Swiss mathematician who lived in the 1700s, and he came up with a bunch of interesting stuff, not the least of which is this. His constant is something like 0.57712. If you add the log of 75 and .577 you come up with 4.89.

TOM: So choice two, approximately five hours is the correct answer.

RAY: Yes. I should add that I didn't want to identify the person that sent the puzzler in, but his answer was bo-oh-oh-gus, and I didn't use it, but I believe that this answer is a lot better.

Who's our winner?

TOM: Our winner this week is Christian Schmidt from Fort Collins, Colorado, and for having his answer selected at random from among all the correct answers that we got, Christian gets a 26-dollar gift certificate to the Shameless Commerce Division at cartalk.com, with which he can get our collection of favorite stories called, Once Upon a Car Fire.

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