The speed of the motorcyclist is 30 km / h uphill and 90 km / h downhill. Determine the average speed of the rider

| July 15, 2021 | education

The speed of the motorcyclist is 30 km / h uphill and 90 km / h downhill. Determine the average speed of the rider for the entire trip if the downhill is twice as long as the uphill.

V1 = 30 km / h.

V2 = 90 km / h.

S2 = 2 * S1.

Vav -?

To find the average speed of a motorcyclist, Vav, it is necessary to divide the entire path S traveled by the time of his 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 rise, t2 is the time of movement during the descent.

t1 = S1 / V1.

t2 = S2 / V2 = 2 * S1 / V2.

t = S1 / V1 + 2 * S1 / V2 = (S1 * V2 + 2 * S1 * V1) / V1 * V2 = S1 * (V2 + 2 * V1) / V1 * V2.

S = S1 + S2 = S1 + 2 * S1 = 3 * S1.

Vav = 3 * S1 * V1 * V2 / S1 * (V2 + 2 * V1) = 3 * V1 * V2 / (V2 + 2 * V1).

Vav = 3 * 30 km / h * 90 km / h / (90 km / h + 2 * 30 km / h) = 54 km / h.

Answer: the average speed of a motorcyclist is Vav = 54 km / h.



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