1/3 of the time the train moves at a speed of 48 km / h, and the rest of the time – at a speed of 72 km / h.

| January 10, 2021 | education

1/3 of the time the train moves at a speed of 48 km / h, and the rest of the time – at a speed of 72 km / h. Find the average speed for the entire time of movement.

V1 = 48 km / h.
V2 = 72 km / h.
t1 = t / 3.
Vav -?
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.
Since on the first part of the path it moved for time t1 = t / 3, then on the second part of the way it moved time t2 = t – t1 = 2 * t / 3.
The entire traversed path S can be represented as a sum: S = S1 + S2, where S1 is the path of the first part of the path, S2 is the path of the second part of the path.
S1 = V1 * t1 = V1 * t / 3.
S2 = V2 * t2 = V2 * 2 * t / 3.
S = V1 * t / 3 + 2 * V2 * t / 3 = (V1 + 2 * V2) * t / 3.
Vav = (V1 + 2 * V2) * t / 3 * t = (V1 + 2 * V2) / 3.
Vav = (48 km / h + 2 * 72 km / h) / 3 = 64 km / h.
Answer: the average train speed is Vav = 64 km / h.



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