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 their first crossing A has swum
30 and B has swum
x - 30 , where x is the pool length.
At their second crossing A has now
swum x + 20 in all and B
has swum 2x - 20
There respective distances will keep
in a fixed ratio because their speeds are in a fixed ratio.
This equation expresses that
x is zero or 70, and a pool of length
zero is not our interest here so 70 m is the pool's length.
Here's another line
of reasoning :
At first crossing A and B have swum
one length between them, and A swam 30m of that length.
At second crossing A and B have swum
two more lengths between them, so A will have swum 60m of those two lengths.
A has swum 90m in all, and that is one whole
length plus a further 20m .
So the pool is 70m