Overtake problem

One truck which is long 6m, velocity 80 km/h started overtaking another truck which is 15m long and with velocity 65 km/h. How long does overtaking last, and how far is faster truck from initial postition if overtaking starts and ends when two trucks are at distance 30m?

Solution:
d₁=6m
v₁=80 km/h
d₂=15m
v₂=65 km/h
d=30 m












When slower truck pass path s₂=v₂t, faster car pass:
s₁=v₁t=d+d₂+v₂t+d+d₁
from which we can calculate t,





Faster car from his initial position pass:

s₁=v₁t=432 m

We can see that if relative speed v₁-v₂ is less overtaking time is growing.