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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.
Dean's Mountain
Age 11 to 14
ShortChallenge Level 
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.
This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.
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