From point A to point B, the distance between which is 410 km, a car drove off. Half an hour later

From point A to point B, the distance between which is 410 km, a car drove off. Half an hour later, a motorcyclist drove out to meet him from point B at a speed of 10 km / more. Find the speed of the car and the motorcyclist if it is known that they met at a distance of 210 km from point A.

х km / h – vehicle speed;

(x + 10) km / h – the speed of the motorcyclist;

The car traveled 210 km before the meeting, the motorcyclist traveled the distance:

410 – 210 = 200 (km);

210 / h – time of movement of the car before meeting with the motorcyclist;

200 / (x + 10) h – the time of the motorcyclist’s movement before meeting the car;

210 / x – 200 / (x + 10) = 1/2;

2 * 210 * (x + 10) – 2 * 200 * x = x * (x + 10);

420 x + 4200 – 400 x = x² + 10 x;

x² – 10 x – 4200 = 0;

D = 100 + 16800 = 16900;

x = (10 ± √16900): 2;

x = – 60 – does not correspond to the condition of the problem;

x ‘= 70; x + 10 = 80;

Vehicle speed 70 km / h; the speed of the motorcyclist is 80 km / h.