### Walk and Ride

How far have these students walked by the time the teacher's car reaches them after their bus broke down?

### Fence It

If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

### How Far Does it Move?

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects the distance it travels at each stage.

# Speeding Up, Slowing Down

##### Stage: 3 Challenge Level:

Congratulations to those of you who managed to find the right answer.

Robyn from the Katherine Semar Junior School was one of the first to send in a correct answer:

The shape is a pentagon, the radius is 30, the dot is on the middle of the bottom left sloping edge.

Robert and Joel from Cowbridge Comprehensive also sent in correct solutions.
Here is Robert's nice piece of detective work:

The graph had four lines before it repeated, but since one was twice as long as the others, the shape had to have five sides.

Since the speed was never zero, the dot could not have been on a corner of the shape, but in the middle of a side.

Robert goes on to consider on which side of the pentagon the dot must have been placed:

The speed of the dot would have been slowest as the side it was on came onto and off the ground.

Since the line that marked the lowest speed (which was twice as long as the others) was the last line before the graph repeated itself, the dot had to be on the side that came off the ground last.

Therefore, the shape that made that graph was a pentagon, of radius 30, with the dot in the middle of the lower left side.

Thank you Cristina, from City of London School for Girls, for sending us a very comprehensive solution