Train Times Quiz Puzzle Answers

Last Friday I travelled on the 9.00 am train from Ayton to Seaview. The train averaged 40 mph over the whole journey, but was much slower on the climbs through the rolling hills between the two towns.

I returned the day after on the 9.00 am train, a new express and the average speed for the return journey was 60 mph, and we had a long stop in Beeborough! Beeborough is exactly halfway between Ayton and Seaview.

Given the information above, can you say with complete certainty any of the following are true:

  1. The average speed for the round-trip journey was 50 mph,
  2. On the return journey the average speed from Seaview to Beeborough was more than 30 mph,
  3. On Friday I arrived in Beeborough later in the day than I did on my return journey,
  4. At some time on Saturday I passed through the same point at exactly the same time as I passed through that point the previous day.

The answers are as follows:

  1. No, this is not true. If Ayton and Seaview are 120 miles apart then Friday's journey took three hours and Saturday's journey took two hours. Overall the 240 mile trip took five hours giving a 48 mph average speed.
  2. Yes, this is true. Again, if Ayton and Seaview are 120 miles apart then it is 60 miles from Seaview to Beeborough. At 30 mph this would take two hours. But we know from 1. above that the entire Seaview to Ayton journey took two hours, so the average speed must have been more than 30 mph.
  3. No, you cannot be certain. The train could have raced to Beeborough on Friday, and then been very, very slow through the hills.
  4. Yes, this must be the case. Imagine two films taken on the two different days of the two train journeys. If these were superimposed they would show two trains travelling towards each other until they met. At the point in time that are at the same place on the track.


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