## 160. Math Puzzle $9 / 78$

On the 70 km long motorway stretch between Dresden and Karl-Marx-Stadt, some vehicles travel at an average speed of 70 km/h, while others travel at an average speed of 100 km/h. How much time do the faster vehicles save?

Is the speeding worth it, considering that the frequency and severity of accidents at 100 km/h are twice as high as at 70 km/h?
The travel time of the slower car was 60 minutes ( $70 \mathrm{~km} : 70 \mathrm{~km} / \mathrm{h} = 1 \mathrm{~h}$ ), that of the faster one 42 minutes ( $70 \mathrm{~km} : 100 \mathrm{~km} / \mathrm{h} = 0.7 \mathrm{~h}$ ).

The time savings of 18 minutes does not outweigh the doubled accident risk.

![](https://cdn.mathpix.com/cropped/2024_06_06_69be9c4355ed0dc2557cg-55.jpg?height=383&width=397&top_left_y=1142&top_left_x=361)