Two cars drove out of two cities A and B at the same time towards each other at constant speeds.

Two cars drove out of two cities A and B at the same time towards each other at constant speeds. The first car arrived in town 16 hours after the meeting, and the second in town A 25 hours after the meeting. How long does it take for the first one to travel from A to B?

1. Distance between cities: S km;

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

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

4. Before the meeting, the first car drove: S1 km;

five . The second car has driven: S2 km;

Ratio: S1 / S2 = V1 / V2;

6. After the meeting, the first car arrived in city B in: T1 = 16 hours;

T1 = (S2 / V1) = 16 hours;

7. The second car arrived in city A in: T2 = 25 hours;

T2 = (S1 / V2) = 25 hours;

8. Attitude:

T2 / T1 = (S1 / V2) / (S1 / V2) = (S1 / S2) * (V1 / V2) = (V1 / V2) * (V1 / V2) =

V1 ^ 2 / V2 ^ 2 = 25/16;

(V1 / V2) ^ 2 = (5/4) ^ 2;

V1 = (5/4) * V2, respectively S1 = S2 * (5/4);

9. The first car will travel from city A to city B in: T hour;

T = S / V1 = (S1 + S2) / V1 = (S2 * (5/4) + S2) / V1 = (S2 / V1) * ((5/4) + 1) =

T1 * (9/4) = 16 * (9/4) = 36 hours.

Answer: The first car travels from A to B in 36 hours.