When does the jam start?

Classical Mechanics Level 3

Imagine a road with two cars, each of length $L$ . Car 1 gets on the road at $t = 0$ moving at $v_{1}$ , and car 2 gets on the road at $t = t_{2}$ , moving at $v_{2} > v_{1}$ .

At what time does the front of car 2 to get in contact with the back of car 1?

Solve for the case where

$v_{1} = 20\text{ m/s}, v_{2} = 25 \text{ m/s}, t_{2} = 100 \text{ s}$ , and $L = 5 \text{ m}$ .

Express your answer in seconds.