a man starts at the bottom of a hill at 7am, and gets to the top at 7pm. his speed varies. the next day he starts at the top at 7pm and gets to the bottom at 7pm. again, his speed varies. he takes the same route. prove that at one point during his return journey, he will be at the same point at the same time as the day before.

some guy from my school at his interview for cambridge for maths a few years ago. the answer i've got is correct (it is!), but it could be explained better...i just can't think how to explin it better...:p

I think you have a typo in the Q. Otherwise the answer is stated in the question - he is at the top on both days at 7pm😛

You're right, kingofthe303. Genius, just picture two people, one starting at one end at 7am and the other at the other. They both walk in opposite directions, at varying speed, reaching their respective goals at 7pm. Since it is obvious that they'll meet on the way (be at the same place at the same time), the desired result follows.

Originally posted by royalchicken
You're right, kingofthe303. Genius, just picture two people, one starting at one end at 7am and the other at the other. They both walk in opposite directions, at varying speed, reaching their respective goals at 7pm. Since it is obvious that they'll meet on the way (be at the same place at the same time), the desired result follows.

Originally posted by genius
yeah-that's the answer i had. although my maths teacher was arguing against it for a while...twas funny...and yeah-there was a typo-bottom at 7am day one and 7pm day two, and top at 7pm day one and 7pm day two...

Originally posted by royalchicken
What was your teacher's objection?