You are driving at 35 m/s east and notice another car that is initially located 462 m in front of you and is moving east at 25 m/s. how far do you travel before you pass the other car?

The easiest way to answer this question is by realizing there are relating the velocities of the two cars. To tackle this problem, you have to understand the picture.  Car 1 travels at 35m/s and Car 2 travels at 25m/s.  Based on relative velocities, we can understand that Car 1 travels 10m/s faster than Car 2 every second.  So we can interpret Car 1's relative velocity to Car 2 as 10m/s.  Car 1 needs to travel 10m/s till a point of catching up to Car 2 which is 462m away.

v = 10m/s

d = 462m

v = d/t

(10) = (462)/t

t = 46.2s

So it takes 46.2 seconds for Car 1 to catch up to Car 2, but the question is asking how far does Car 1 travel to catch up.  So we have to use Car 1's velocity and not the relative velocity:

v = 35m/s

v = d/t

(35) = d/(46.2)

d = 1617m

Car 1 traveled a total distance of 1617m.