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 60 km / h. What is the average speed (in km / h) of the car along the way?

S1 = S / 4.

t1 = t / 2.

S2 = S / 3.

t2 = t / 4.

V3 = 60 km / h.

Vav -?

Vav = S / t.

S1 / V1 = t1.

S / 4 * V1 = t / 2.

S2 / V2 = t2.

S / 3 * V2 = t / 4.

S3 = S – S1 – S2 = S – S / 4 – S / 3 = S * (1 – 1/4 – 1/3).

t3 = t – t1 – t2 = t – t / 2 – t / 4 = t * (1 – 1/2 – 1/4).

V3 = S3 / t3 = S * (1 – 1/4 – 1/3) / t * (1 – 1/2 – 1/4) = Vav * (1 – 1/4 – 1/3) / (1 – 1/2 – 1/4) = Vav * 5 * 4/12 * 1 = 5 * Vav / 3.

Vav = 3 * V3 / 5.

Vav = 3 * 60 km / h / 5 = 36 km / h.

Answer: the average speed of the vehicle along the entire path is Vav = 36 km / h.