The car travels the first third of the way at a speed V1, and the rest of the way at a speed V2 = 50 km / h.

The car travels the first third of the way at a speed V1, and the rest of the way at a speed V2 = 50 km / h. Determine the average speed on the first section of the route, if the average speed along the entire route is Vav = 37.5 km / h.

Given:
V2 = 50km / h,
s1 = S / 3,
Vav = 37.5 km / h;
Find: V1 -?
The average speed of the body is equal to the ratio of the total path traversed by the body to the entire time of movement:
Vav = S / (t1 + t2);
Here;
t1 = s1 / V1 = S / (3 * V1)
and
t2 = s2 / V2;
s2 = S – s1 = 2 * S / 3;
t2 = 2 * S / (3 * V2);
From here we get:
Vav = S / [S / (3 * V1) + 2 * S / (3 * V2)] =
= 3 / (1 / V1 + 2 / V2) = 3 * V1 * V2 / (V2 + 2 * V1);
12.5 * (50 + 2 * V1) = 50 * V1;
V1 = 25km / h.