Four vehicles travelled on a road with constant velocities. The car
overtook the scooter at 12 o'clock, then met the bike at 14.00 and
the motorcycle at 16.00. The motorcycle met the scooter at 17.00
then it overtook the bike at 18.00. At what time did the bike and
the scooter meet?
The illustration shows the graphs of fifteen functions. Two of them have equations y=x^2 and y=-(x-4)^2. Find the equations of all the other graphs.
The illustration shows the graphs of twelve functions. Three of
them have equations y=x^2, x=y^2 and x=-y^2+2. Find the equations
of all the other graphs.
adopted an approach based on a graphical solution and using similar
triangles. I have included his graph, for interest, below. I used a
graphical approach to solve this problem the first time I met it -
and I felt that my solution was quite a neat one.
The last solution, and easily the most
elegant, was presented by Ian and Charlie of the William Lovell
School. I have added a little to their solution for clarity but it
is simple and uses no algebra - quite a surprise and very, very
nice as it makes excellent use of proportionality.
The negative sign for $y$ has happened because
James assumed the second bus was the fastest when it was actually
the first bus.
Here is the diagram Derek
used for his solution. Although his final answer was wrong, the use
of similar triangles can result in a reasonably elegant