Hi,
I remember reading a great math problem in a precalculus book a few
years ago and I'd like to find that problem. I believe it was sent to
Einstein to solve and it took him a minute to realize that the math
didn't compute. It went something like this:
There are two cars, one can go up the hill at 10 miles per hour and
down the hill at 15 mph and has a 30 minute head start. How fast does
the other car have to go to reach the destination at the same time.  I
can't remember the exact numbers and wording, but the problem ends up
working out that it's impossible for the second car to catch the first
car...I hope you can find the problem!

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Clarification of Question by progress4u-ga on 27 Jan 2005 15:02 PST

There was a distance given as well, like 2 miles up and 3 miles down
or something like that.

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Clarification of Question by progress4u-ga on 01 Feb 2005 07:03 PST

It's not Zeno's paradox/tortoise & achilles. It's a d=rt problem where
the second car can't ever catch the first car because it would have to
travel backward in time...now that I think about it, I don't think
there was a head start. They leave at the same time up the hill, but
car A travels at a slower rate. Car B goes faster still on the way
down the hill so that it reaches the bottom before A reaches the top.
Which makes it impossible for A to catch B. I may have to track down
that old precalculus book...thanks for the help though!

I doubt that people put maths questions in terms of cars in Einstein's
time. But anyway, the problem you describe sounds very much like a
variant on the well known Zeno's paradox. Search Google for that, and
you'll find stacks of interesting stuff that may relate to your math
problem.

This is the closest I could find:

ACHILLES AND THE TORTOISE (use find to locate "two cars" on the page)
http://www.thinkartlab.com/pkl/archive/GUNTHER-BOOK/SF_PAR3.html

~~Cynthia

There was a similar problem put to Einstein that he tried to - or
could not - solve using calculus.
Simplified:  Two vehicles are approaching each other at different
speeds, starting a stated distance from one another.  A bird (or
something moving significantly faster than the vehicles) starts with
them, from where one of the vehicles starts, and flies to the other,
turning with no time lost for the turn, flying back to the other
vehicle, and so on until the vehicles meet.
How far had the bird flown?

Maybe it can be solved with calculus, but that's not necessary (Your
pre-calc source).  You just need to figure the time that it takes for
the vehicles to meet and use that to compute the distance the bird
could fly at its speed in that period.
Could that be your problem?

There is a similar one  - of you like such:
Given the dimensions of a roll of toilet paper(radius of the tube and
outer edge  of the roll, thickness and length of each piece of
T-paper), how many pieces of T-paper are there spiralled on the roll
(ignoring the wrapper that says there are 400)?
It's a nice calculus problem, but a lot easier, just calculate the
volume and divide by the volume of one piece of T-paper.
For years (too late to ask him now) I have been wondering if my Dad,
who mentioned the problem and solved such, recognized this solution.
Good luck!