Two buses simultaneously departed from point A to point B. One of them traveled at the speed v1 for the first

| September 17, 2021 | education

Two buses simultaneously departed from point A to point B. One of them traveled at the speed v1 for the first half of the journey, and at the speed v2 for the second half. The second bus moved at speed v1 for the first half of its travel time from A to B, and for the second half at speed v2. Determine the average speed of each bus if v1 = 30 km / h, and v2 = 40 km / h.

V1 = 30 km / h.

V2 = 40 km / h.

S1 = S / 2.

S2 = S / 2.

t1 = t / 2.

t2 = t / 2.

Vav1 -?

Vср2 -?

To find the average speed of the bus, Vav, it is necessary to divide the entire path of movement S by the entire time of movement t: Vav = S / t.

Let us express the travel time of the bus along the entire route: t = t1 + t2, where t1 is the travel time on the first half of the route, t2 is the travel time on the second half of the route.
t1 = S1 / V1 = S / 2 * V1.

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

Vav1 = S / (t1 + t2) = S / (S / 2 * V1 + S / 2 * V2) = S * 2 * V1 * V2 / S * (V1 + V2) = 2 * V1 * V2 / (V1 + V2).

Vav1 = 2 * 30 km / h * 40 km / h / (30 km / h + 40 km / h) = 34.3 km / h.

Let us express the path traveled by the bus: S = S1 + S2.
S1 = V1 * t1 = V1 * t / 2.

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

Vav2 = S / t = (S1 + S2) / t = (V1 * t / 2 + V2 * t / 2) / t = (V1 + V2) * t / 2 * t = (V1 + V2) / 2.

Vav2 = (30 km / h + 40 km / h) / 2 = 35 km / h.

Answer: Vav1 = 34.3 km / h, Vav2 = 35 km / h.



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