The motorcycle traveled 90 km at a speed of 30 km / h, and then another 40 km at a speed of 20 km / h

| May 30, 2021 | education

The motorcycle traveled 90 km at a speed of 30 km / h, and then another 40 km at a speed of 20 km / h. What is the average speed of the entire path?

V1 = 30 km / h.

S1 = 90 km.

V2 = 20 km / h.

S2 = 40 km.

Vav -?

To find the average speed of a motorcyclist, Vav, it is necessary to divide the entire path S traveled by him by the time of his 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 part of the path, t2 is the time of movement on the second part of the path.

Time with uniform motion is expressed by the formulas: t1 = S1 / V1, t2 = S2 / V2.

t = S1 / V1 + S2 / V2 = (S1 * V2 + S2 * V1) / V1 * V2.

S = S1 + S2.

Vav = (S1 + S2) * V1 * V2 / (S1 * V2 + S2 * V1).

Vav = (90 km + 40 km) * 30 km / h * 20 km / h / (90 km * 20 km / h + 40 km * 30 km / h) = 26 km / h.

Answer: the average speed of a motorcyclist is Vav = 26 km / h.



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