## 298. Math Puzzle $3 / 90$

Sebastian visits his grandmother every week, who lives in the neighboring town 10 km away. Most of the time, he rides his bicycle. On a nice day, it takes the grandmother's favorite grandson 1 hour and 20 minutes to get to the destination and back.

One day, however, a strong wind is blowing. The boy still sets off on his bike.

The speed increases by $4 \mathrm{~km} / \mathrm{h}$ on the way there, and decreases by the same amount on the way back. Sebastian thinks that this does not change his travel time? Is he right?
Without wind, the speed is $\frac{s}{t}=\frac{20 \mathrm{~km}}{1 \frac{1}{3} \mathrm{~h}}=15 \mathrm{~km} / \mathrm{h}$.

With the wind, it takes $t=\frac{s}{v}=\frac{10 \mathrm{~km}}{19 \mathrm{~km} / \mathrm{h}} \approx 31.6 \mathrm{~min}$ and against the wind $t=\frac{s}{v}=$ $\frac{10 \mathrm{~km}}{11 \mathrm{~km} / \mathrm{h}} \approx 54.5 \mathrm{~min}$, in total thus $86.1 \mathrm{~min}$, and therefore 6.1 min longer.