From point a to point b, the distance between which is 120 km, two cars simultaneously drove towards each other

From point a to point b, the distance between which is 120 km, two cars simultaneously drove towards each other with constant speeds V1 = 90 km / h and V2 = 110 km / h. At what distance from point A will the cars meet?

Given:

S (AB) = 120 kilometers – distance between points A and B;

v1 = 90 km / h – the speed of the vehicle leaving point A;

v2 = 110 km / h – the speed of the car leaving point B to point A.

It is required to determine L (km) – the distance from point A at which cars will meet.

Let the origin of the coordinate system be point A. Then the equations of motion of cars will have the form:

S1 (t) = v1 * t;

S2 (t) = S (AB) – v2 * t.

Let’s find the meeting time of two cars by equating the equations of motion:

S1 (t) = S2 (t);

v1 * t = S (AB) – v2 * t;

v1 * t + v2 * t = S (AB);

t * (v1 + v2) = S (AB);

t = S (AB) / (v1 + v2) = 120 / (90 + 110) = 120/200 = 0.6 hours.

Since the first car left point A, then:

L = v1 * t = 90 * 0.6 = 54 kilometers.

Answer: cars will meet at a distance of 54 kilometers from point A.