**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 using 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.