From two settlements located at a distance of 5 km, a car and a motorcycle begin to move in one direction

From two settlements located at a distance of 5 km, a car and a motorcycle begin to move in one direction at the same time. The speed of the car is 30 km / h and the speed of the motorcycle is 20 km / h. How long will it take for a car to catch up with a motorcycle?

S = 5 km = 5000 m.
Vav = 30 km / h = 8 1/18 m / s.
Vmot = 20 km / h = 5 5/9 m / s.
t -?
Sа = Vа * t.
Smot = Vmot * t.
Sв = S + Smoot.
Vav * t = S + Vmot * t.
Vav * t – Vmot * t = S.
(Vav – Vmot) * t = S.
t = S / (Vav – Vmot).
t = 5 km / (30 km / h – 20 km / h) = 0.5 h = 30 min = 1800 s.
Answer: the car will catch up with the motorcycle in t = 0.5 h = 30 min = 1800 s.