Optimal Start Time Given Different Distanced Paths

I have no idea what kind of math this falls under, but heres the problem:

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Assuming all cars mentioned below are moving at constant speed.

Assume that the road looks like this:

X -> A,B,C -> D

Road A splits into three separate roads (A, B, C) of different distances, then merges at one point to be a single road D. The time to get from X->A->D is = 1 minutes, X->B->D = 2 minutes, X->C->D = 3 minutes".

If there are 3 parked cars at the beginning X with each car taking a respective road (A, B, C)

What is the best time spacing such that the cars are as closely spaced (Ex: Each car after car1 should leave P seconds after each other) that each car should move such that when the three cars are driving on road D, they are at least greater than 10 seconds apart? (Note that the best case is desired)

Problem Asks to find P.

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