The distance between settlements A and B is 65 km. The pedestrian left point A to point B at exactly 12:00.

The distance between settlements A and B is 65 km. The pedestrian left point A to point B at exactly 12:00. An hour later and from point B, a cyclist left for point A. Exactly 3 hours after the cyclist left, they met. Determine the speed of the pedestrian and cyclist.

Since the cyclist was on the way for 3 hours, and the pedestrian left an hour earlier, it means that the pedestrian was on the way for 4 hours. Let the speed of the pedestrian be x and the speed of the cyclist equal to y.

4x – pedestrian path, 3y – cyclist’s path, 4x + 3y = 65.

Let’s solve the equation by selecting:

x = 1; 65 – 4 * 1 = 61 (not divisible by 3).

x = 2; 65 – 4 * 2 = 57; 57: 3 = 19.

x = 3; 65 – 4 * 3 = 53 (not divisible by 3).

x = 4; 65 – 4 * 4 = 49 (not divisible by 3).

x = 5; 65 – 4 * 5 = 45; 45: 3 = 15.

x = 6; 65 – 4 * 6 = 41 (not divisible by 3).

x = 7; 65 – 4 * 7 = 37 (not divisible by 3).

x = 8; 65 – 4 * 8 = 33; 33: 3 = 11.

Answer: Possible options: pedestrian speed 2 km / h, cyclist speed 19 km / h.

Or a walking speed of 5 km / h, a cyclist’s speed of 15 km / h.

Or pedestrian speed 8 km / h, cyclist speed 11 km / h.