Problem 183 Solution

Suppose the husband usually took the train that arrived at 5:00, but today took the one that arrived at 4:00. Since the wife would have spent all her time driving at the same speed it stands to reason she saved 10 minutes both directions because her husband walked part of the way.

So, if the wife usually arrived at the station at 5:00 then she would have spotted her husband at 4:50. The husband started walking at 4:00, thus he would have spent 50 minutes walking.

My thanks to MathGent for this elegant solution.