L D[AR2P#0.0]
Lifetime Supporting Member
Third puzzle in the tunnel theme:
Answers by PM
Code:
Two cats are travelling on a train, the train is running at constant speed.
The cats are initially stationary in the middle of the train.
The train enters a tunnel. A little later,
at the moment the cats enter the tunnel,
one cat starts running towards the front of the train and
the other cat starts running towards the rear of the train.
The cats run at the same speed.
The cat running towards the front of the train stops when it exits the tunnel.
Similarly, the cat running towards the rear of the train stops
when it exits the tunnel.
The cats are now separated by distance A
(the cats are not limited to integer steps)
If the speed of the train is √3 times the speed of the cat,
what is the length of the tunnel as a proportion of A?
What is the minimum length of the train as a proportion of A?
Give your answers using expressions containing surds.
For example, (but wrong)
Length of tunnel= A(66+√3),
Minimum length of train = A√3/77
Answers by PM