The car traveled the distance from point A to point B at a speed of 70 km / h, and back

| May 1, 2021 | education

The car traveled the distance from point A to point B at a speed of 70 km / h, and back – at a speed of 60 km / h. What is the average ground speed of a vehicle?

V1 = 70 km / h.

V2 = 60 km / h.

S1 = S2.

Vav -?

To find the average ground speed Vav, it is necessary to divide the entire path S traveled by the car by the time of its passage 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 from point A to point B, t2 is the time of movement from B to A.

t1 = S1 / V1 = S1 / V1.

t2 = S2 / V2 = S1 / V2.

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

We express the entire traversed path S by the formula: S = S1 + S2 = 2 * S1.

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

Vav = 2 * 70 km / h * 60 km / h / (60 km / h + 70 km / h) = 64.6 km / h.

Answer: the average road speed of the vehicle was Vav = 64.6 km / h.



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