49. A TRAIN PILE - UP 
The little Australian town of Giles rested peacefully in the early morning light. The long straight gleam of the east-west line cut the Nullabor like a knife, and cleanly bisected the little settlement.
As was his custom, Eric waited patiently where the dusty path crossed the shiny metal. It was several months since he had given up his work on the line, but the railway was still his life. At various times, day and night, Eric would leave his little cottage, and wander down to the track, waiting, sometimes for hours, for the mighty express to thunder through. Then, satisfied, he would return home with his memories. But Eric was puzzled. Although his visits to the line were at random times, nine times out of ten the express which came through was travelling westwards.
‘Either Perth is stockpiling a mass of rolling stock, or I’m going barmy!’ he muttered to himself.
Perhaps you can provide the real explanation.
Solution
Let us consider some possible train timetables. Suppose first that the east-bound train passes through Giles at midnight, and the west-bound train at noon. Then if Eric stands by the rail at random times, there is a 50% chance of either train passing. For if he arrives in the twelve hours before noon, it will be the west-bound, and if he arrives in the twelve hours after noon it will be the east bound.
Some reflection now shows that Eric’s problem is actually what one might expect to happen. As an extreme case, suppose that the west-bound train passes Giles at noon, and the east-bound train passes Giles five minutes later. Now the only chance Eric has of seeing the east-bound train is if he arrives at the line during those five minutes after noon.
In the actual problem, we might have the west-bound train passing at noon, and the east-bound train passing at 2.24 in the afternoon. For, dividing 24 hours into tenths gives 2 hours 24 minutes, and 2.24 pm breaks the period from noon to noon in the ratio 1:9.
