The bus traveled a third of the way at a speed of 20 km / h, half of the remaining distance at a speed of 30 km / h

The bus traveled a third of the way at a speed of 20 km / h, half of the remaining distance at a speed of 30 km / h, and the rest of the way at a speed of 60 km / h. Determine the average speed along the way.

Problem data: S1 (first part of the path) = 1/3 S; S2 (second part of the path) = (S – 1/3 S) / 2 = 1/3 S; S3 (third part of the path) = 1/3 S; S1 (first speed) = 20 km / h; V2 (second speed) = 30 km / h; V3 (third speed) = 60 km / h.

Average speed of this bus along the entire route: Vav. = S / (t1 + t2 + t3) = S / (S1 / V1 + S2 / V2 + S3 / V3) = S / (S / 3V1 + S / 3V2 + S / 3V3) = 1 / (1 / 3V1 + 1 / 3V2 + 1 / 3V3).

Calculation: Vav. = 1 / (1 / (3 * 20) + 1 / (3 * 30) + 1 / (3 * 60)) = 1 / 0.05 = 30 km / h.