The Asymmetric Commute

Oct 01, 2007

RAY: The essence of this puzzler was sent in fairly recently by someone named Miles Benson. Anyway, I had to monkey with it a bit.

I overheard a conversation between two young fellows one morning while at the local coffee shop and they were discussing their jobs and one of them said, "I set my trip odometer the first day I started my job and the round trip is exactly 20 miles."

"Wow, that's great," the other guy says. "I wish my job was only 10 miles from home."

"Oh, no," number one guy says, "it's only 5 miles to get to work, but 15 miles to get home."

"What are you driving, an ice cream truck or something like that?"

"No, no, no, no."

"Oh, I know, you're taking a detour to visit your girlfriend."

"Nope, not at all. I drive directly from home to work, taking the shortest route. And I return from work, also taking the shortest route. No detours, no side trips. I come directly home and it's 15 miles to get home, making it a 20-mile round-trip to work and home from work."

And he goes on to say: "Last week the boss called and asked me to report to another location for a few days to fill in for someone who was on vacation. Ready for this? On those days I drove 15 miles to get to work, but then the ride home was only 5 miles."

The question is - how can this be?
RAY: I guess there are other possible answers than the one that we came up with, but let's assume that guy number one works at some place like a fast-food restaurant on the highway. So he gets on the highway --

TOM: Yeah.

RAY: -- near his house, drives five miles to work.

TOM: This is what I thought.

RAY: But to get home, he's got to drive to the next exit which is five miles away.

TOM: To turn around and come back.

RAY: Five miles away from home, another five miles just to get to the opposite side of the highway where he was working.

TOM: That's 10.

RAY: And then five miles to his house.

TOM: Fifteen.

RAY: So 5 miles out; 15 miles to get back home. The day the boss asked him to report to the other location, it was the Burger King directly across the highway from what he usually worked at, in which case it was 15 miles to get to work --

TOM: And five miles to get back.

RAY: Pretty good, huh?

TOM: I love it.

RAY: Do we have a winner?

TOM: Yeah, we have a winner. The winner this week is Mike Brickseus from Springfield, Oregon. And for having his answer selected at random from among all the correct answers that we got, Mike will get a 26-dollar gift certificate to the Shameless Commerce Division at, with which he can get our new four-CD set; four complete shows called Four Perfectly Good Hours.

RAY: As in you've just wasted four perfectly good hours, right?

TOM: Exactly. That's yours, Mike, for being this week's puzzler winner, and congratulations.

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