Average velocity with a relay race

[kx250f341]

Homework Statement

A relay race is run along a straight-line track of length 300.0 m running south to north. The first runner starts at the south end of the track and passes the baton to a teammate at the north end of the track. The second runner races back to the start line and passes the baton to a third runner who races 300.0 m northward to the finish line. The magnitudes of the average velocities of the first, second, and third runners during their parts of the race are 7.06 m/s, 7.00 m/s, and 7.51 m/s, respectively. What is the average velocity of the baton for the entire race? [Hint: You will need to find the time spent by each runner in completing her portion of the race.]

Homework Equations

Vavg= delta r/delta t

delta r= rf-ri
delta t=tf-ti

The Attempt at a Solution

7.06m/s=300m/T
T=42.4929 sec

7.00m/s=300m/T
T=42.85714 sec

7.51m/s=300m/T
T=39.9467 sec

After these I get confused which one is the final and initial displacement because there are three of them. Any help please?

 

[Delphi51]

average velocity = total distance divided by total time.
The total distance is 900 meters.

 

[kx250f341]

So Delphi51 you say to get the answer it would be 900m/125.296sec= 7.518 m/s

But I am doing my h.w. online and it marks it incorrect?

 

[SammyS]

NO! Average velocity is (Displacement)/(Time).

The Displacement is a VECTOR. The displacement for the race is: The VECTOR from the starting line to the finish line. At the end of the race, the baton is 300 meters NORTH of where it was at the start.

 

[Delphi51]

The word "velocity" sometimes means displacement/time and sometimes means distance/time. When it means the former, you must express the velocity as a vector - magnitude and direction. So the final answer would be 300/7.518 North.