A student walks from X to Y in $20$ minutes at a speed of $3.0\ \text{km h}^{-1}$. At Y, she turns through $90^\circ$ and then walks for $15$ minutes at $4.0\ \text{km h}^{-1}$ to arrive at Z. What is her average speed from X to Z?
- A$2.4\ \text{km h}^{-1}$
- B$3.4\ \text{km h}^{-1}$
- C$3.5\ \text{km h}^{-1}$
- D$5.0\ \text{km h}^{-1}$