A California Coastal Cruise

Jun 23, 2008

RAY: This was sent in by someone named Jim Blecksmith and I didn't even mess with it that much! He wrote:

"My honey and I took a trip recently from Los Angeles to Monterey for a short vacation, a weekend getaway. We left L.A. on a Friday morning at 7:10. The first 201 miles of the trip was on Highway 101 and we traveled at the normal freeway speed limit, plus a little, when we could. At San Luis Obispo, we turned onto Highway 1 for the remaining 136 miles to Monterey.

"Highway 1 is a beautiful, but narrow and winding road that follows the coastline so our speed was of course much slower. We were eager to get to Monterey so we only made the necessary fuel and schnerdling stops and arrived Friday afternoon at 2:35. We had a wonderful time walking along Cannery Row, visiting the Aquarium, and exploring the Steinbeck Museum in Salinas.

"On Monday we got up, had a leisurely breakfast, and left at 9:20. We took the same route back to L.A. but this time, we were not in any hurry. We stopped many times to take pictures and enjoy the scenic coastline along Highway 1. We arrived at home in L.A. Monday evening at 6:10.

"So we left L.A. at 7:10 on Friday morning and arrived at Monterey at 2:35 in the afternoon and we drove 337 miles to do that. And then on Monday morning we left Monterey at 9:20 and drove those same 337 miles and got back to L.A. at 6:10."

Here's the question: "What's the probability that there was a place along our route that we reached at the same time of day on our trip to Monterey and the return trip to L.A.? And by the way we pretty much obeyed the speed limits."
RAY: So remember the obfuscating details? We took the same route there as we did getting back, a total of 337 miles each way. But here's the question, what is the probability that there was a place along our route that we reached at the exact same time of day on our trip to Monterey and our return trip from Monterey? What's the probability?

TOM: Wow, that's great. That sounded so complicated.

RAY: Well, it did except not really.

TOM: Luckily there's no calculations that we can do.

RAY: No. You got to just shoot for it. Here's the answer, here's the way to look at it. You're going to superimpose the two trips. Assume that you have twins that are leaving Monterey on the same day that you are leaving L.A.

TOM: Got it.

RAY: OK, they're leaving two hours later. And where you cross paths is that place. You have to pass each other, the only way you might not pass each other is this. If you left L.A. at 7:10 and you got to Monterey at 9:19 a.m. OK. So you did it in what, an hour and nine minutes.

TOM: Right.

RAY: OK. Then you wouldn't meet along the way, but that would require that you exceeded the speed limit, in fact I'm pretty sure in order to do that you'd have to travel like 160 miles an hour.

TOM: Right. Otherwise you're going to pass each other.

RAY: But I stated in the original puzzle that we pretty much obeyed the speed limit, and if you obey the speed limit there is no way that you can't pass, so the answer is the probability that you do this --

TOM: A hundred-percent!

RAY: Exactly. So who's our winner?

TOM: The winner this week is Maggie Zeeman from Atlanta, Georgia, and for having her answer selected at random from the pile of correct answers that we got, Maggie gets a 26-dollar gift certificate to the Shameless Commerce Division at cartalk.com, with which she can get our brand-new four-CD set, Field Guide to the North American Whacko.

RAY: Congratulations, Maggie, on your enormous win today!

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