Can anyone help with an average speed problem?

[wtp08]

Homework Statement

A racing team of 3 drivers drove a 24 hour event in shifts. The first driver drove only one fourth of the race but averaged 140km/hr. The second driver drove one third of the race at an average speed of 170 km/hr. The last driver drove the remainder of the race at 160 km/hr. What was the average speed of the team?

Homework Equations

I do not know how to set up the problem in order to find average speed since there is no specific distance

The Attempt at a Solution

 

[Millacol88]

Well, this is kind of an odd question. I would think that a weighted average could work. E.g. multiply the first speed by 1/4, the second by 1/3, and the third by 5/12. Then add these numbers together. See if that gives you the right answer, I'm not entirely sure.

 

[Uthobin]

You have the total time: T=24h
Then, t₁=$\frac{1}{4}$T=6h
t₂=$\frac{1}{3}$T=8h
t₃=$\frac{5}{12}$T=10h

The distance of each shift:
d₁=v₁*t₁
d₂=v₂*t₂
d₃=v₃*t₃

Now you have the total distance and the total time, so you can calculate the average speed.