What is the average speed of the train on the stretch between two stations, if the first half of the distance between

| May 8, 2021 | education

What is the average speed of the train on the stretch between two stations, if the first half of the distance between the stations it traveled at an average speed of 50 km / h, and the second at an average speed of 70 km / h.

V1 = 50 km / h.

V2 = 70 km / h.

S1 = S2 = S / 2.

Vav -?

To find the average speed of movement Vav, it is necessary to divide the entire path traveled by the train S by the time of its movement t along the entire path: 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 km / h.

Answer: the average speed of a train on the stretch is Vav = 58 km / h.



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