On the first half of the journey, the bus moved at a speed 8 times higher than on the second.

On the first half of the journey, the bus moved at a speed 8 times higher than on the second. The average speed of the bus along the entire route is 16 km per hour. Determine the speed of the bus on each section of the route.

Initial data: V1 (speed of the bus on the first half of the journey) = 8V2 (speed on the second half of the journey); Vav / (average speed) = 16 km / h; S1 = S2 = 0.5S.
1) The speed of the bus in question on the second half of the journey: Vav. = S / t = S / (t1 + t2) = S / (S1 / V1 + S2 / V2) = S / (S / (2 * 8V2) + S / 2V2) = 1 / (1 / 16V2 + 1 / 2V2) = 1 / (9 / 16V2), whence V2 = 9Vav. / 16 = 9 * 16/16 = 9 km / h.
2) Speed on the first half of the journey: V1 = 8V2 = 8 * 9 = 72 km / h.

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