# The speed of the train on the ascent is 30 km / h, and on the descent is 90 km / h.

**The speed of the train on the ascent is 30 km / h, and on the descent is 90 km / h. Determine the average speed for the entire section of the track, if the descent is twice as long as the ascent.**

Vp = 30 km / h.

Vsp = 90 km / h.

Ssp = 2 * Sп.

Vav -?

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

The travel time of the entire path is expressed by the sum: t = tp + tp, where tp is the time of movement on the rise, tp is the time of movement on the descent.

tp = Sp / Vp.

tsp = Ssp / Vsp = 2 * Sp / Vsp.

t = Sп / Vп + 2 * Sп / Vп = (Sп * Vsp + 2 * Sп * Vп) / Vп * Vsp = Sп * (Vsp + 2 * Vп) / Vп * Vsp.

S = Sп + Sп = Sп + 2 * Sп = 3 * Sп.

Vav = 3 * Sp * Vp * Vsp / Sp * (Vp + 2 * Vp) = 3 * Vp * Vp / (Vp + 2 * Vp).

We will find the average train speed by the formula: Vav = 3 * Vp * Vsp / (Vsp + 2 * Vp).

Vav = 3 * 30 km / h * 90 km / h / (90 km / h + 2 * 30 km / h) = 54 km / h.

Answer: the average train speed was Vav = 54 km / h.