For the first quarter of its journey, the Mercedes was moving at an average speed of 120 km / h

| January 11, 2021 | education

For the first quarter of its journey, the Mercedes was moving at an average speed of 120 km / h, and the rest of the way – at an average speed of 100 km / h. Determine the average speed of the Mercedes along the entire route.

V1 = 120 km / h.
S1 = S / 4.
S2 = 3 * S / 4.
V2 = 100 km / h.
Vav -?
The average speed of movement Vav of a Mercedes is determined by the formula: Vav = S / t, where S is the entire path of the vehicle, t is the time of movement along the entire path.
The time of movement along the entire path is t = t1 + t2, where t1 is the time of movement on the first part, t2 is the time of movement on the second part.
Let’s find the time of movement on the first and second part of the path: t1 = S1 / V1 = S / 4 * V1, t2 = S2 / V21 = 3 * S / 4 * V2.
Vav = S / (S / 4 * V1 + 3 * S / 4 * V2) = 4 * V1 * V2 / (V2 + 3 * V1).
Vav = 4 * 120 km / h * 100 km / h / (100 km / h + 3 * 120 km / h) = 104.4 km / h.
Answer: the average speed of a Mercedes is Vav = 104.4 km / h.



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