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

From point A to point B, the distance between which a pedestrian came out 13 km. Simultaneously with him, a cyclist left B for A. The cyclist was driving at a speed of 11 km / h higher than the speed of 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.

1. The distance between points A and B is equal to: S = 13 km;

2. The meeting point is removed from point B by: Sb = 8 km;

3. Pedestrian speed is equal to: Vn km / h;

4. Cyclist speed: Vb = (Vn + 11) km / h;

5. The cyclist made a stop on the way: To = 0.5 hours;

6. The pedestrian covered the path: Sn = S – Sb = 13 – 8 = 5 km;

7. His travel time: Tn hour;

8. Cyclist spent time: Tb hour;

9. We compose the equation of the time of movement:

Tn – Tb = To;

Sn / Vn – Sb / Vb = To;

5 / Vn – 8 / (Vn + 11) = 0.5;

55 – 3 * Vn = 0.5 * Vn * (Vn + 11);

Vn² + 17 * Vn – 110 = 0;

Vn1.2 = -8.5 + – sqrt ((- 8.5) ² + 110) = -8.5 + – 13.5;

A negative root is meaningless;

Vn = -8.5 + 13.5 = 5 km / h.

Answer: the pedestrian speed is 5 km / h.