*Challenge question #25 (22/08/2016)*

**Junior Question**

One hour after leaving home, a car had engine troubles. The car then had to travel the remaining trip at $\tfrac{3}{5}$ of its original speed and arrived at its destination $2$ hours late. If the mishap had occurred $50$ km further along, the car would have arrived $40$ minutes sooner. How fast was the car travelling originally?

**Senior Question**

Show that no equilateral triangle inscribed in a non-circular ellipse can have its centroid coincide with the centre of the ellipse.