From point A to point B, the distance between which is 13 km, a pedestrian came out. At the same time

From point A to point B, the distance between which is 13 km, a pedestrian came out. At the same time, a cyclist left B to A to meet him. The cyclist was driving at a speed 11 km / h higher than the speed of a pedestrian, and made a half-hour stop along the way. Find the speed of the cyclist if it is known that they met 5 km from point A.

The pedestrian and the cyclist met 5 km from point A, which means that by the time of the meeting, the pedestrian had covered 5 km, and the cyclist had traveled 13 – 5 = 8 km.

Let the speed of the pedestrian be x km / h, then the speed of the cyclist is x + 11 km / h.

According to the condition of the problem, the cyclist was in motion 1/2 hour less, which means we can make the following equation:

5 / x – 1/2 = 8 / (x + 11),

(10 – x) / 2 * x = 8 / (x + 11),

16 * x = 10 * x + 110 – x² – 11 * x,

– x² – 17 * x + 110 = 0.

The discriminant of this equation is:

(-17) ² – 4 * (-1) * 110 = 729.

Since x can only be a positive number, the problem has a unique solution:

x = (17 – 27) / – 2 = 5 (km / h) – pedestrian speed,

5 + 11 = 16 (km / h) – the speed of the cyclist.