# The UKMT Senior Challenge-I

Rachel and Nicky stand at either end of a straight athletics track. They then run at constant (but different) speeds to the other end of the track, turn and run back to their original end at the same speed they ran before. On their first leg, they pass each other $$20$$ m from one end of the track. When they are both on their return leg, they pass each other for a second time $$10$$ m from the other end of the track. How many metres long is the track?

This problem is not original.This problem is part of this set.

×