Henry Ernest Dudeney/Puzzles and Curious Problems/65 - The Pedestrian Passenger/Solution

Puzzles and Curious Problems by Henry Ernest Dudeney: $65$

A train is travelling at the rate of $60$ miles per hour.

A passenger at the back of the train wishes to walk to the front along the corridor,

and in doing so walks at the rate of three miles per hour.

At what rate is the man travelling over the permanent way?

The puzzlingly obvious answer is: $63$ miles per hour.

Dudeney seems to believe that the result is somehow counterintuitive or paradoxical.

Let $\mathbf v_T$ be the velocity of the train relative to the railway.

Let $\mathbf v_P$ be the velocity of the passenger relative to the train.

Then the velocity of the passenger relative to the railway is $\mathbf v_T + \mathbf v_P$.

The result follows when you plug in the numbers.

$\blacksquare$