An average velocity question dealing with a relay race - Please help ASAP

Question

The cheetah can run as fast as 113 km/h, the falcon can fly as fast as 161 km/h, and the sailfish can swim as fast as 105 km/h. The three of them run a relay with each covering a distance L at maximum speed.

a)What is the average speed of this relay team for the entire relay?

b) Compare this average speed with the numerical average of the three individual speeds. (Give you answer as a multiple of vav.)

c)Explain carefully why the average speed of the relay team is not equal to the numerical average of the three individual speeds.

Answer 1

a.  The formula for speed is:  distance = speed*time

Solved for time, the formula is:  time = distance/speed

time that each animal went was:

Cheetah = L/113

Falcon = L/161

Sailfish = L/105

To find the average speed, we need to divide the total distance traveled by the total time that was used.

v_av = Distance total/Time total

v_av = (L + L + L)/(L/113 + L/161 + L/105)

v_av = 3L/(16,905L/1,910,265 + 11,865L/1,910,265 +18,193L/1,910,265)

v_av = 3L/(46,963L/1,910,265)

v_av = 3L(1,910,265)/46,963L

v_av = 122.1 km/h

b.  To find the numerical average of the 3 speeds, just add the speeds together and divide by 3

(113 + 161 + 105)/3

379/3

129.7 km/h

To compare the two, we need to make a ratio:  122.1/129.7

This approximates to .941.

c.  The reason that these numbers are not the same is that the animals did not spend the same time in each leg of the relay.  The average velocity is a ratio of distance covered to time spent covering it.  Since the animals each spent a different amount of time in their leg of the race, the speed of each animal factored differently into the average speed of the team.