Dean's mountain
Dean runs down the mountain at 12 km per hour. How long does it take him to run down the mountain?
Age
11 to 14
Challenge level
Problem
Dean runs up a mountain road at 8 km per hour. It takes him one hour to get to the top.
He runs down the same mountain at 12 km per hour. How long does it take him to run down the mountain?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
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.