Determine the distance between the starting and ending point of the rider if in the first 30 km he drove at a speed of 15

Determine the distance between the starting and ending point of the rider if in the first 30 km he drove at a speed of 15 m / s and then turned and drove perpendicular to the original direction at a speed of 72 km / h. The average speed for the entire movement is 64.8 km / h.

We denote:
S₁ and S₂ – the path before and after the turn,
t₁ and t₂ – travel time before and after the turn,
V₁ and V₂ – speed before and after the turn,
Vc – average speed.
t₁ = S₁ / V₁ = 30,000 m / 15 m / s = 2000 s.
S₂ = V₂ * t₂;
Vc = (S₁ + V₂ * t₂) / (t₁ + t₂);
Vc * t₁ + Vc * t₂ = S₁ + V₂ * t₂;
t₂ = (Vc * t₁ – S₁) / (V₂ – Vc);
V₂ = 72 km / h = 72000 m / 3600 s = 20 m / s;
Vc = 64.8 km / h = 64800 m / 3600 s = 18 m / s;
t₂ = (18 m / s * 2000 s – 30,000 m) / (20 m / s – 18 m / s) = 3000 s.
S₂ = 20 m / s * 3000 s = 60,000 m.
S = √ ((30,000 m) ² + (60,000 m) ²) = 67,082 m = 67.1 km.
Answer: 67.1 km.