Puzzle ZBVT 

Workings

Hint
The gap between the two options is 2 hours.

Answer
The distance must have been sixty miles.

If Sir Edwyn left at noon and rode 15 miles an hour, he would arrive at four o'clock – an hour too soon. If he rode 10 miles an hour, he would arrive at six o'clock – an hour too late. But if he went at 12 miles an hour, he would reach the castle of the wicked baron exactly at five o'clock – the time appointed.

The text above is the answer given in the book, and below is a method of finding the answer.

If we call the distance to the castle, D and use the fact that Time = Distance ÷ Speed, we have:

Travelling at 15 mph:

   Time1 = D ÷ 15           (an hour too soon)

Travelling at 10 mph:

   Time2 = D ÷ 10           (an hour too late)

The time gap between these two times is 2 hours, therefore

   Time2 – Time1 = 2

   D ÷ 10 – D ÷ 15 = 2

Multiply throughout by 30:

   3D – 2D = 60

   D = 60 miles.