Two cars leave at the same time from points A and B towards each other on the same road.

Two cars leave at the same time from points A and B towards each other on the same road. The first car arrives at point B 15 hours after departure, and the second arrives at point A 4 hours after their meeting. How long did it take from the moment the cars left until the moment they met, if both cars were moving at a constant speed?

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

2. Speed ​​of the first car: V1 km / h;

3. Speed ​​of the second car: V2 km / h;

4. Time of movement of cars until the moment of meeting: T hour;

5. Travel time after departure of the first car: T1 = 15 hours;

6. The second car will cover this distance in: T2 hours;

7. Time of movement of the second car after the meeting: Tb = 4 hours;

8. Vehicle speeds:

V1 = S / T1 km / h;

V2 = S / T2 = S / (T + Tb) km / h;

9. Let’s calculate the path through the total speed of cars: V km / h;

S = V * T = (V1 + V2) * T =

((S / T1) + (S / (T + Tb)) * T =

S * T * (1 / T1 + 1 / (T + Tb));

10. There is one variable left (T):

T * (1 / T1 + 1 / (T + Tb)) = 1;

T * (1/15 + 1 / (T + 4)) = T * (T + 4 + 15) / (15 * (T + 4) = 1;

T ^ 2 + 19 * T = 15 * T + 60;

T ^ 2 + 4 * T – 60 = 0;

T1,2 = -2 + – sqrt ((- 2) ^ 2 + 60) = -2 + – 8;

A negative root is meaningless;

T = -2 + 8 = 6 hours.

Answer: 6 hours have passed from the moment the cars left until the moment they met.