Train Station

Question

Trains on the Glasgow Subway depart every 4 minutes, and a complete circuit takes 24 minutes. Ewan sets off at 8.30 am on a train round in one direction at the same time as another train leaves in the opposite direction. How many trains will he pass on a complete circuit back to his starting station? (Do not count trains at the start or end station.)

Answer 1

So, Evan's train starts out and takes 24 minutes to complete the circuit.

 

Using T=0 for the starting time of Evan's train, Evan's train will complete the circuit at T=24.  The train starting in the opposite direction at T=24 is not counted.  At approximately T=12(depending on speeds), Evan's train will pass the train that started in the opposite direction at T=0.  Evan's train also passes the trains that had started before T=0.

 

So, Evan's train will pass the trains that started in the opposite direction at:

  T =     -20  -16  -12   -8   -4   0  4  8  12  16  20

 

Since the problem stated, "Do not count trains at the start or end station", the train that left in the opposite direction at T=0 was not counted at that time, it was counted when Evan's train passed it at T=approximately 12 (depending on speed of trains).

 

Evan's train passes 11 trains.

 

Answer 2

Draw a diagram!

At time zero, 5 trains are in the circuit.

As Ewen train travels another 5 leave the station.

 

He see 10 total.