# The car drove the first quarter of the way at a constant speed for half of the entire travel time.

**The car drove the first quarter of the way at a constant speed for half of the entire travel time. The next third of the way, moving at a constant speed, in a quarter of the time. The rest of the way was covered at a speed of υ3 = 100 km / h. What is the average speed of the vehicle along the way? What are the speeds in the first and second sections?**

Given: S1 = 1/4 S; t1 = 1/2 t; S2 = 1/3 S; t2 = 1/4 t; S3 = S – (S1 + S2) = 5/12 S; t3 = t – (t1 + t2) = 1/4 t; V3 = 100 km / h.

1) S1 / V1 = t1; S / 4V1 = t / 2.

2) S2 / V2 = t2; S / 3V2 = t / 4.

3) S3 / V3 = t3; 5S / 12V3 = t / 4; 5S / 1200 = t / 4; S = 60t.

4) First speed: 60t / 4V1 = t / 2; 60 / 4V1 = 1/2; 60 = 2V1; V1 = 30 km / h.

5) Second speed: 60t / 3V2 = t / 4; 60 / 3V2 = 1/4; 3V2 = 60 * 4 = 240; V2 = 80 km / h.

6) Average speed: V = 1 / (1 / 4V1 + 1 / 3V2 + 5 / 12V3) = 60 km / h.