### On the Road

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?

### Escalator

At Holborn underground station there is a very long escalator. Two people are in a hurry and so climb the escalator as it is moving upwards, thus adding their speed to that of the moving steps. ... How many steps are there on the escalator?

### Illusion

A security camera, taking pictures each half a second, films a cyclist going by. In the film, the cyclist appears to go forward while the wheels appear to go backwards. Why?

# There and Back

##### Stage: 4 Challenge Level:

In this problem, consider the following:
When Brian swims with the flow, his total speed is his speed in the water plus the speed of the moving water. When he swims against the flow, his total speed is the difference between his speed in still water and the speed of the moving water.

This leads to the following solution:

Let the speed of the river be v , distance to the moored boat = d , and the time to complete the downstream journey = t .

 Downstream Upstream Speed of man = 3 v Speed of man = v Distance = d Distance = d Time = t Time = 12 - t

Again, using distance = speed x time, gives the following equations:

(1) d = 3 vt

(2) d = v (12- t )

combining (1) and (2) gives

3 vt = v (12 - t )

which leads us to t = 3 minutes

Using this information tells us that the speed of the river is d/9

and since Brian swims at twice this speed, his speed in the still water is 2d/9.

He swims a distance of 2 d at this speed.

So it will take him 9 minutes.

Correct solutions were sent from Nicholas and Adrian (South Greenhoe Middle School).