[Guest]

A man drove from Detroit to Chicago, leaving at 8 in the morning. The next day he leaves Chicago at 8 and drives the same highway back to Detroit. If his speed varies, will there be any spot along the route that he passes at exactly the same time each day?

There has to be. To see it clearly, imagine two men driving the route on the same day, one leaving Detroit at 8 and the other leaving Chicago at 8. They have to pass each other at some point, and they'll be there at the same time.

[Guest]

A man drove from Detroit to Chicago, leaving at 8 in the morning. The next day he leaves Chicago at 8 and drives the same highway back to Detroit. If his speed varies, will there be any spot along the route that he passes at exactly the same time each day?

There has to be. To see it clearly, imagine two men driving the route on the same day, one leaving Detroit at 8 and the other leaving Chicago at 8. They have to pass each other at some point, and they'll be there at the same time.

In case of two people they will definitely cross each other but not necessarily at the same point and at the same time of the day as speed varies.

They can meet but not always on the same point and at the same time....

[Molly Mae]

A man drove from Detroit to Chicago, leaving at 8 in the morning. The next day he leaves Chicago at 8 and drives the same highway back to Detroit. If his speed varies, will there be any spot along the route that he passes at exactly the same time each day?

There has to be. To see it clearly, imagine two men driving the route on the same day, one leaving Detroit at 8 and the other leaving Chicago at 8. They have to pass each other at some point, and they'll be there at the same time.

There will be a single point n somewhere along the highway where, yes, he passed at the exact same time of the previous day. Imagine the man drives from Detroit to Chicago. The next day, when he leaves at 8 from Chicago to Detroit, a ghost of his previous journey begins again from Detroit (think Mario Kart time trials). He and the ghost must eventually pass each other. Where they meet is point n and they will both be there at the same time (hour and minute, but not day).

Edited July 22, 2011 by Molly Mae