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.
Two cyclists, practising on a track, pass each other at the
starting line and go at constant speeds. If you record the times
each takes to complete a lap can you devise a method for finding
when and where they will meet? You may like to start by supposing
they take 72 seconds and 80 seconds respectively to complete a lap.
Notice that with these lap times they meet for the first time at
the starting line. When and where do they meet if the lap times are
70 seconds and 85 seconds? Can you find other lap times that are
such that the cyclists meet exactly half way round the track.