From point A to point B, the distance between which is 40 km, a motorist and a cyclist left at the same time.

| February 11, 2021 | education

From point A to point B, the distance between which is 40 km, a motorist and a cyclist left at the same time. It is known that a motorist travels 50 km more per hour than a cyclist. Determine the speed of the cyclist if it is known that he arrived at point B 3 hours 20 minutes later than the motorist.

1. Distance between points: S = 40 km;

2. Speed of the motorist: Vа km / h;

3. Cyclist speed: V in km / h;

4. According to the problem: Va = (Vв + 50) km / h;

5. Driving time of the motorist: That hour;

6. Cyclist trip time: TV hour;

7. By the condition of the problem:

TV – Ta = 3 hours 20 minutes (10/3 hours);

TV – Ta = S / Vv – S / Va = S / Vv – S / (Vv + 50) =

40 / Vv – 40 / (Vv + 50) = 10/3;

200 / (Vв * (Vв + 50)) = 1/3;

Vv ^ 2 + 50 * Vv – 600 = 0;

Vв1,2 = -25 + – sqrt (25 ^ 2 + 600) = -25 + – 35 $

A negative root is meaningless;

Vv = -25 + 35 = 10 km / h.

Answer: the speed of the cyclist is 10 km / h.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.