Help With Physics - Constant Velocity?

Question

I am having trouble tackling this problem:
"A car makes a 60.0-km trip with an average velocity of 40.0 km/h in a direction due north. The trip consists of three parts. The car moves with a constant velocity of 25 km/h due north for the first 15 km and 62 km/h due north for the next 32 km. With what constant velocity (magnitude and direction) does the car travel for the last 13-km segment of the trip?"

Here's what I've done so far:
40 km/h =(25 km/h + 62 km/h + x) / 3

120 km/h = 25 km/h + 62 km/h +x

120 km/h = 87 km/h + x
33 km/h = x
^not even sure if thats the correct way to do it. any help will be highly appreciated!!!!!

Answer 1

You can't just average the speeds. The distances and times have to be considered.
Total time T = X/V(ave) = 60 km/40 (km/h) = 1.5 h
T = t1 + t2 + t3
t1 = 15/25 = 0.6 h
t2 = 32/62 = 0.516 h
t3 = 1.5 - 0.6 - 0.516 = 0.384 h
x3 = 13 km
v3 = x3/t3 = 13/0.384 = 33.85 km/h
Although this is close to your answer, a more extreme example shows how inaccurate speed averaging can be. Say I drive 100 km at 100 km/hr (1 hr) and 100 km at 1 km/hr (100 hrs). Average speed = (100+1)/2? No way. I took 101 hrs to go 200 km, average speed < 1/2 km/hr.