Problem of the Week
Problem E
There and Back

Silvan and Nash are training for a race. They run $600$ m along a straight path from their school to a bridge. Once they reach the bridge they turn around and run along the same path back to their school. Silvan and Nash run at different, but constant speeds for each part of the run. For each of them, their constant speed from the bridge back to the school was twice their constant speed on the way to the bridge.

Silvan reached the bridge first, turned around, and immediately started running back to school. Silvan then passed Nash running in the opposite direction when they were $50$ m away from the bridge.

When Silvan reaches the school, how far behind him will Nash be?