It seems like the solution to the puzzler about the trip from LA to Monterey and back did not meet the criteria. Didn’t the Puzzler say there HAD to be one spot on the trip that you passed at the same time of day? Or did I misread it? If I didn’t, I think the answer is wrong. There is not necessarily one spot that you’ll reach at the same time of day northbound and southbound. The only way that could be true, it seems to me is if either the speeds and times of departure are constant or if more is known about the exact speeds during each leg. Am I wrong?
It seems like the solution to the puzzler about the trip from LA to Monterey and back did not meet the criteria. Didn’t the Puzzler say there HAD to be one spot on the trip that you passed at the same time of day? Or did I misread it? If I didn’t, I think the answer is wrong. There is not necessarily one spot that you’ll reach at the same time of day northbound and southbound. The only way that could be true, it seems to me is if either the speeds and times of departure are constant or if more is known about the exact speeds during each leg. Am I wrong?
That is what it said. You didn’t misread it. And you are wrong.
As long as both your departure times are before both your arrival times, and you take the same route, there will always be some point on that you hit at the same time on both parts of the trip.
The simplest way to prove this to yourself is probably to just do it by hand. Draw a line, call one end “LA” and the other “Monterey”. Have something to represent cars. Have the cars leave LA and Monterey whenever you want (as long as they both leave before one of them arrives at their destinatoin), and then try to not have them meet somewhere on the line.
Wait a second. Certainly, if a car left LA at 7:10 driving north and a car left Monterery at 9:20 heading south, they’d meet somewhere along the route. But they wouldn’t always meet at the same place; where they met would depend on driving speed and length of stops. So I still am not convinced. Thanks for your response, though.
Agreed, the “same time of day” part of the question seems to make finding the real puzzler answer much more complex.
How would you word the question then to express the same idea? Namely what are the odds that there is some point on the road where if you stood there and wrote down the times when the car passed on each of its trips, that those two times would be the same?