# On the first half of the route, the bus moved at a speed 4 times faster than on the second. The module of the average

On the first half of the route, the bus moved at a speed 4 times faster than on the second. The module of the average speed of the bus on the entire route is 32 km / h. Determine the modules of the bus speed for each half of the route.

Data: V1 (bus speed on the first half of the route) = 4V2 (speed on the second half of the route); Vav. (the module of the average bus speed on the entire route) = 32 km / h.
1) The speed on the second half of the route is calculated from the formula: Vav. = S / (t1 + t2) = S / (S / 2V1 + S / 2V2) = 1 / (1 / 8V2 + 1 / 2V2) = 1 / (1 / 8V2 + 1 / 2V2).
32 = 1 / (1 / 8V2 + 1 / 2V2).
32 = 1 / (5 / 8V2).
32 = 8V2 / 5.
V2 = 32 * 5/8 = 20 km / h.
2) Speed on the first half of the route: V1 = 4V2 = 4 * 20 = 80 km / h.

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