Dean's Mountain

Answer: 40 minutes

On the way up Dean runs at $8\text{km/h}$ for $1$ hour.
The distance is therefore: $\text{Distance} = \text{Speed} \times \text{Time} = 8\text{km/h} \times 1\text{h} = 8\text{km}$.

On the way down, he runs at $12\text{km/h}$.
The time is therefore: $\text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{8\text{km}}{12\text{km/h}} = \frac{2}{3}\text{h}$

Therefore it takes Dean $40$ minutes to run down the mountain.