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. 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.

Let the speed of a cyclist leaving point B to point A be x km / h, then the speed of a pedestrian leaving point A to point B will be (x – 11) km / h, since it is known from the condition of the problem that the cyclist was traveling at a speed , 11 km / h higher pedestrian speed. The cyclist and the pedestrian met 5 km from point A, which means that the pedestrian was on the way for 5 / (x – 11) hours, and the cyclist 5 / (x – 11) – ½, since the cyclist made a half-hour stop on the way. On the other hand, the distance between points A and B is 13 km, of which the cyclist traveled 13 – 5 = 8 (km) in 8 / x hours. We get the equation:
5 / (x – 11) – ½ = 8 / x;
Let us simplify the fractional rational equation by reducing its terms to a common denominator, after reducing similar terms, we obtain a quadratic equation:
х² – 5 ∙ х – 176 = 0;
we will solve the quadratic equation, for this we will find the discriminant D = 729;
x₁ = – 11 – does not satisfy the condition of the problem;
x₂ = 16 (km / h) – the speed of the cyclist.
Answer: The cyclist’s speed is 16 km / h.