by Howard Williams
Published July 28 2019 (link)
Sarah and Jenny are runners who train together on a circular track, and Sarah can run up to 20 per cent faster than Jenny. They both run at a constant speed, with Sarah running an exact percentage faster than Jenny. To reduce competition they start at the same point, but run round the track in different directions, with Sarah running clockwise.
On one day they passed each other for the seventh time at a point which is an exact number of degrees clockwise from the start. Sarah immediately changed her pace, again an exact percentage faster then Jenny. After a few passes both runners reached the exit, at a point on the track an exact number of degrees clockwise from the start, at the same time.
How fast, relative to Jenny, did Sarah run the final section?