A 1 metre cube has one face on the ground and one face against a
wall. A 4 metre ladder leans against the wall and just touches the
cube. How high is the top of the ladder above the ground?
In this problem we are faced with an apparently easy area problem,
but it has gone horribly wrong! What happened?
Straight lines are drawn from each corner of a square to the mid
points of the opposite sides. Express the area of the octagon that
is formed at the centre as a fraction of the area of the square.
If the track length is L then you can write down the speeds and
the distance between the cyclists at any given time in terms of L.
The cyclists meet when the relative distance covered is a multiple
of L. You might like to model this using a cardboard tube and
threads. Think of the length of the tube as the time axis and the
threads around the tube showing the cyclists path on the track.