60. Riding in windy weather. A cyclist takes 3 minutes to travel 1 km if the wind is at his back, and 4 minutes if he has to ride against a headwind. How long will it take him to travel 1 km if the wind dies down? Someone might say that since the arithmetic mean of 3 and 4 is $3 \frac{1}{2}$, the cyclist will need $3 \frac{1}{2}$ minutes, but this solution is incorrect.
60. The cyclist will cover one kilometer in \(3 \frac{3}{7}\) minutes, or at a speed of \(\frac{7}{24}\) km/min. The wind changes his speed by \(\frac{1}{24}\) km/min. Therefore, with the wind, he moves at a speed of \(\frac{8}{24}\) km/min, and against the wind - at a speed of \(\frac{6}{24}\) km/min, so he covers 1 km in 3 and 4 minutes respectively, as claimed.