Question 25

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?

Answer

The car was originally travelling at $50$ km h$^{-1}$.

Worked Solution

Senior Question

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

Hint

The vertices of such a triangle would also have to lie on a circle with the same centre.

Worked Solution