In the first 0.5 h, the cyclist covered 10 km, for the next 12 minutes he rode at a speed of 25 km / h

In the first 0.5 h, the cyclist covered 10 km, for the next 12 minutes he rode at a speed of 25 km / h The remaining 9 km at a speed of 18 km / h. What is the average speed of a cyclist A) throughout the entire journey? B) in the first half of the journey.

Given:

S1 = 10 km

T1 = 0.5 h

V2 = 25 km / h

T2 = 12 min = 0.2 h

S3 = 9 km

V3 = 18 km / h

To find:

A) Vav =?

B) Vav in the first. ½ way =?

Decision:

Let’s find the total time and all the way:

Stot = S1 + S2 + S3 = 10 km + 5 km + 9 km = 24 km,

S2 = V2 * T2 = 25 km / h * 0.2 h = 5 km;

T = T1 + T2 + T3 = 0.5 h + 0.2 h + 0.5 h = 1.2 h,

T3 = S3 / V3 = 9 km / 18 km / h = 0.5 h;

A) Find the average speed over the entire section:

Vav = Stot / T = 24 km / 1.2 h = 20 km / h.

B) Find the average speed of the cyclist in the first half of the journey:

Vav in the first. ½ way = (Stotal / 2) / TV first. ½ way = 12 km / 0.58 h = 20.7 km / h,

TV first ½ way = T1 + T2 * 2/5 = 0.5 h + 0.2 h * 0.4 = 0.5 h + 0.08 h = 0.58 h.

Answer: A) Vav = 20 km / h; B) Vav in the first. ½ way = 20.7 km / h.