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?
Brian swims at twice the speed that a river is flowing, downstream
from one moored boat to another and back again, taking 12 minutes
altogether. How long would it have taken him in still water?
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?
At first glance it may seem surprising that the two given
distances fix the length of the pool. This context will also
stimulate visualisation, as students 'picture' the motion of each
swimmer and then watch for the moments when they cross.
Why wasn't the second crossing in the same place as the
If the swimmers can keep this going indefinitely will they have
eventually had a crossing point everywhere along the length of the
What happens if they both swim twice as fast?
What would happen if the pool was twice as long?