## 277. Math Puzzle $6 / 88$

An aircraft requires exactly 30 minutes to fly from A to B and back again in calm weather at a speed of $v=200$ $\mathrm{km} / \mathrm{h}$.

How does the flight time change if there is a wind blowing from A towards B with an airspeed of $w=50 \mathrm{~km} / \mathrm{h}$?
The distance between A and B is: $s=\frac{1}{2} v \cdot t=50 \mathrm{~km}$; for the round trip, 30 minutes are required.

Due to the wind, the flight speeds change as follows: $(200+50) \mathrm{km} / \mathrm{h}$ with tailwind and $(200 - 50) \mathrm{km} / \mathrm{h}$ with headwind. The flight times are calculated using the formula $t=s / v$.

$$
t=\frac{50 \mathrm{~km}}{250 \mathrm{~km} / \mathrm{h}}+\frac{50 \mathrm{~km}}{150 \mathrm{~km} / \mathrm{h}}=0.20 \mathrm{~h}+0.33 \mathrm{~h}=0.53 \mathrm{~h}=31.8 \mathrm{~min}
$$

Due to the wind, the total flight time increases by almost two minutes.