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

From point A to point B, the distance between which is 13 km, a pedestrian came out. Simultaneously with him, a cyclist left B for A. The cyclist was traveling at a speed 11 km / h faster than a pedestrian, and made a half-hour stop along the way. Find the speed of the pedestrian if it is known that they met 8 km from point B.

Let the speed of the pedestrian be x km / h, then the speed of the cyclist is (x + 11) km / h. The cyclist traveled 8 km in 8 / (x + 11) hours before meeting the pedestrian, and the pedestrian covered 13 – 8 = 5 km in 5 / x hours before the meeting. The travel time of a pedestrian is equal to the travel time of the cyclist, taking into account the half-hour (1/2 hour) stop of the cyclist. Let’s make an equation and solve it.
8 / (x + 11) + 1/2 = 5 / x – bring to a common denominator 2x (x + 11);
(2x * 8) / (2x (x + 11)) + (x (x + 11)) / (2x (x + 11)) = (5 * 2 (x + 11)) / (2x (x + 11 ));
16x + x ^ 2 + 11x = 10x + 110; O.D.Z. x ≠ 0; x ≠ – 11;
x ^ 2 + 16x + 11x – 10x – 110 = 0;
x ^ 2 + 17x – 110 = 0;
D = b ^ 2 – 4ac;
D = 17 ^ 2 – 4 * 1 * (- 110) = 289 + 440 = 729; √D = 27;
x = (- b ± √D) / (2a)
x1 = (- 17 + 27) / 2 = 10/2 = 5 (km / h) – pedestrian speed;
x2 = (- 17 – 27) / 2 = – 44/2 = – 22 speed cannot be negative.
Answer. 5 km / h