average velocity

Question

You drive a car 6 h at 45 km/h, then 6 h at 60 km/h.

 

What is your average velocity?

 

What is your average velocity if you drive a distance of 315 km at a speed of 45 km/h, then the same distance at a speed of 60 km/h?

Answer 1

Distance = Velocity * Time, or D = V * T

 

Break up each trip into 2 parts, D1 and D2.  In the first case, 

D1 = 45 (km/h) * 6 h = 270 km

D2 = 60 (km/h) * 6 h = 360 km

The total distance D = 630 km is covered in 12 h, so the average velocity is 

V = 630 km / (12 h) = 52.5 km/h

 

In the second case you are given that 

D1 = 315 km = 45 (km/h) * T1  ==>  T1 = 315 km / (45 km/h) = 7 h

D2 = 315 km = 60 (km/h) * T2  ==>  T2 = 315 km / (60 km/h) = 5.25 h

The total distance D = 630 km is covered in 12.25 h, so the average velocity is 

V = 630 km / (12.25 h) ~  51.43 km/h