Average speed

Question

Lucy runs the first half of a race at 5kph. Then she picks up her pace and runs the last half of the race at 10kph. What is her average speed on the course in hours?

Answer 1

Suppose the race is 2D km long. 

[1]    D = 5t₁  ... this is the first half of the distance, at 5 km/hr, taking t₁ hours

[2]    D = 10t₂ ... this is the second haf of the total distance, at 0 km/hr, taking t₂ hours.

the total time is t₁ + t₂ =D/5 + D/10.

the average velocity is total distance divided by total time:  (2D) / [3D/10] = 20/3 = 6 2/3 km/hr.

 

Answer 2

Since she ran the same distance at each speed,

the average speed is the average of the two speeds.

 

(5+10)/2 = 7.5 kph