Harel has challenged Lisa to a race. He plans on riding his bicycle,
but Lisa will be driving a car. Both contestants will be traveling at
a constant speed throughout the race, but Lisa's car is significantly
faster than Harel's bicycle. Say that Lisa's car is **k** times as
fast as Harel's bicycle, but **k**>1. This challenge seems to be
not too bright of a move on Harel's part, but he has added the
condition that he be given a 5-minute head start. Assume that the
finish line is very, very VERY far away -- say a zillion miles.

1. Who do you intuitively think will win the race?

Well, just as Lisa was smugly imagining her victory, Harel burst her bubble:

"Wipe that silly grin off your face, Lisa. There is no way you
can win this race; I've tricked you. consider the diagram below of our
positions on the track. H_{0} represents my position at the
starting line. After **t _{1}**=5 minutes, my position will
be H

At sometime, call it **t _{2}**, you will reach the
position L

Now Lisa has gone into seclusion; Harel's argument seems entirely logical, yet it contradicts her firm belief that fiery red hot-rods should beat bicycles in races. She feels forced to choose between mathematical logic and her own concept of the real world. you can help to save her sanity if you find a flaw in Harel's argument.