*Challenge question #17 (27/06/2016)*

**Junior Question**

Walter can walk uphill at $3$ km/h, on flat ground at $4$ km/h, and downhill at $6$ km/h.

It takes Walter $1$ hour to walk from home to the cinema, and then $90$ minutes to walk back home along the same route.

Find the distance between Walter’s house and the cinema.

**Senior Question**

The coordinates of three points A, B, C on the Cartesian plane are all integers.

By considering areas, or otherwise, prove that triangle ABC cannot be equilateral.