# The first third of the way the body moves at a constant speed of 40 km / h, the second – 60 km / h, and the third

The first third of the way the body moves at a constant speed of 40 km / h, the second – 60 km / h, and the third – at a speed of 120 km / h. Determine the average speed along the way.

S1 = S2 = S3 = S / 3.
V1 = 40 km / h.
V2 = 60 km / h.
V3 = 120 km / h.
Vav -?
The average speed of movement Vav is determined by the formula: Vav = S / t, where S is the entire distance traveled, t is the time of the entire movement.
t = t1 + t2 + t3 = S / 3 * V1 + S / 3 * V2 + S / 3 * V3 = S * (V2 * V3 + V1 * V3 + V1 * V2) / 3 * V1 * V2 * V3.
Vav = S / S * (V2 * V3 + V1 * V3 + V1 * V2) / 3 * V1 * V2 * V3 = 3 * V1 * V2 * V3 / (V2 * V3 + V1 * V3 + V1 * V2).
Vav = 3 * 40 km / h * 60 km / h * 120 km / h / (60 km / h * 120 km / h + 40 km / h * 120 km / h + 40 km / h * 60 km / h) = 60 km / h.
Answer: average speed Vav = 60 km / h.

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