The first third of the way the cyclist rode at a speed of 15 km / h.

The first third of the way the cyclist rode at a speed of 15 km / h. The average speed of a cyclist is 20 km / h. How fast did he drive the rest of the way?

s1 = S / 3,
v1 = 15m / s,
v = 20m / s;
v2 -?
Average speed is determined by the ratio of the distance traveled to the elapsed time:
V = S / t;
t = t1 + t2,
where
t1 = s1 / v1 = S / (3 * v1);
s2 = S – s1 = 2 * S / 3;
t2 = s2 / v2 = 2 * S / (3 * v2);
t = (S / 3) * (1 / v1 + 2 / v2);
t = S / V;
(S / 3) * (1 / v1 + 2 / v2) = S / V;
1 / v1 + 2 / v2 = 3 / V;
2 / v2 = 3 / V – 1 / v1 = 3/20 – 1/15 = 1/12;
v2 = 24km / h.