The train travels the first 10 km at a speed of 30 km / h, the second 10 km at a speed of 40 km / h, the third 10 km at a speed of 60 km / h, what is the average speed along the entire route?
S1 = 10 km.
V1 = 30 km / h.
S2 = 10 km.
V2 = 40 km / h.
S3 = 10 km.
V3 = 60 km / h.
To find the average speed of movement Vav, it is necessary to divide the entire distance traveled by the train S by the time of its movement t along the entire path: Vav = S / t.
The entire traversed path S will be the sum: S = S1 + S2 + S3.
S = 10 km + 10 km + 10 km = 30 km.
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.
Since the train moved uniformly on track sections, t1 = S1 / V1, t2 = S2 / V2, t3 = S3 / V3.
t1 = 10 km / 30 km / h = 1/3 h.
t2 = 10 km / 40 km / h = 1/4 h.
t3 = 10 km / 60 km / h = 1/6 h.
t = 1/3 h + 1/4 h + 1/6 h = 9/12 h = 3/4 h.
Vav = 30 km * 4 h / 3 = 40 km / h.
Answer: the average speed of the train along the entire route was Vav = 40 km / h.