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

From point A to point B, the distance between which is 13 km, a pedestrian came out. Half an hour later, a cyclist left B for A at his meeting and was traveling at a speed of 11 km / h more than the speed of a pedestrian. Find the speed of the cyclist if it is known that they met 5 km from point A.

Let’s say that the speed of a pedestrian is x km / h. According to the condition of the problem, he covered 5 km, which means the travel time was 5 / x hours.

Since the distance between A and B is 13 km, the cyclist has traveled:

13 – 5 = 8 km.

The cyclist’s speed is x + 11 km / h, which means he was on the way

8 / (x + 11) hours, but left 0.5 hours later.

Let’s compose and solve the 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 equation has a unique solution:

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

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