Is it possible for two cars to leave an origin at different times and arrive at the destination at the same time?

Alice and Bob both live in point A. Both work in point B.

Every morning, the time it takes to get from A to B, starts at value X, goes up (with rush hour) to Y and then back to X.

Alice and Bob want to see if they can leave at different times in the morning and arrive at the same time. Assume that both drive the highest speed they can give the traffic, and no more than the speed limit.

Can you prove if they can, or cannot? If they can, when?