After the bus passed the first half of the journey, it got into a traffic jam. As a result, its average speed on the second half of the route was 8 times less than on the first route. The average bus speed along the entire route is 16 km / h. Determine the speed of the bus on the second half of the journey
V1 = 8 * V2.
Vav = 16 km / h.
S1 = S2 = S / 2.
To find the average speed of the bus, Vav, it is necessary to divide the entire path S it has traveled 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 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 = S / 2 * 8 * V2 = S / 16 * V2.
t2 = S2 / V2 = S / 2 * V2.
t = S / 16 * V2 + S / 2 * V2 = (S + 8 * S) / 16 * V2 = 9 * S / 16 * V2
Vav = S * 16 * V2 / 9 * S = 16 * V2 / 9.
V2 = 9 * Vav / 16.
V2 = 9 * 16 km / h / 16 = 9 km / h.
V1 = 8 * 9 km / h = 72 km / h.
Answer: on the first half of the journey the average speed of the bus was V1 = 72 km / h, on the second half V2 = 9 km / h.
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