Two cars drove out of two cities at the same time towards each other. It is known that one traveled all the way in 4 hours

Two cars drove out of two cities at the same time towards each other. It is known that one traveled all the way in 4 hours, and the other – in 5. What part of the path was between them 1 hour after the start of the movement?

1. Distance between cities: S km;

2. The first car traveled all the way in: T1 = 4 hours;

3. The second car traveled all the way in: T2 = 5 hours;

4.Relative speed of the first car: V1 km / h:

V1 = S / T1 = (S / 4) km / h;

5. Relative speed of the second car: V2 km / h:

V2 = S / T2 = (S / 5) km / h;

6. After time T = 1 hour from the beginning of the movement, they will pass:

S1 = V1 * T = (S / T1) * T = S * (T / T1) = S * (1/4) km;

S2 = V2 * T = (S / T2) * T = S * (T / T2) = S * (1/5) km;

7. The path left for the cars to travel:

So = S – S1 – S2 = S – S * (1/4) – S * (1/5) =

S – (S * (1/4) + S * (1/5)) = S * (1 – (9/20)) = S * (11/20) km.

Answer: 1 hour after the start of the movement, there was an 11/20 part of the way between the cars.