My friend sets out walking at a speed of $3$ miles per hour. I set out behind her $5$ minutes later at $4$ miles per hour. When I start walking, how many miles has my friend traveled?

Your friend has walked 5 MINUTES ( or 1/12 of an hour) at 3 m/hr

1/12 hr * 3 m/hr = 1/4 mile ahead of you when you start