V1 = 50 km / h.
V2 = 70 km / h.
S1 = S2 = S / 2.
To find the average vehicle speed Vav, it is necessary to divide the entire path S it has traveled by the time of its movement t: Vav = S / t.
The travel time of the entire path is expressed by the sum: t = t1 + t2, where t1 is the time of movement on the first half of the path, t2 is the time of movement on the second half of the path.
t1 = S1 / V1 = S / 2 * V1.
t2 = S2 / V2 = S / 2 * V2.
t = S / 2 * V1 + S / 2 * V2 = (S * V2 + S * V1) / 2 * V1 * V2 = S * (V2 + V1) / 2 * V1 * V2.
Vav = S * 2 * V1 * V2 / S * (V2 + V1) = 2 * V1 * V2 / (V2 + V1).
Vav = 2 * 50 km / h * 70 km / h / (70 km / h + 50 km / h) = 58.3 km / h.
Answer: the average vehicle speed was Vav = 58.3 km / h.
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