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?
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?
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?
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 .
Again, using distance = speed x time, gives the following
(1) d = 3 vt
(2) d = v (12- t )
combining (1) and (2)
3 vt = v (12 - t )
which leads us to t = 3 minutes
Using this information tells us that the speed of the river is
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).