John R. answered • 01/30/13

John R: Math, Science, and History Teacher

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.