Answer
The initial separation distance was 20 meters.
Work Step by Step
Let $v$ be the constant speed of the two cars. During car 1's braking period, car 1's average speed is $\frac{v}{2}$, while car 2's average speed at that time is $v$. Since car 1 moves 10 meters in that time, car 2 moves 20 meters. Car 2 then applies the brakes and moves 10 meters during the braking period.
Car 1 moves a total distance of 10 meters while car 2 moves a total distance of 30 meters. Therefore, the initial separation distance was 20 meters.
