### Home > CALC > Chapter 7 > Lesson 7.1.4 > Problem 7-45

Kimberly and Varag are in a bicycle race. Homework Help ✎

If Kimberly's velocity in miles per hour during the race is

*v*(*t*) = 2.3sin^{t}, find the bicyclist's average velocity during 0 ≤ *t*≤ 6. Describe your method.If Varag's distance from the starting line during the race is

*s*(*t*) = 20*t*+ 2 sin(*t*), find his average velocity during 0 ≤*t*≤ 6. Describe your method.When is each bicyclist traveling at his/her average velocity?

For parts (a) and (b), each is a different application of Mean Value. Pay attention to the given information and read carefully.

See Math Notes below.

Average Velocity = 16.102 mph

Average Velocity = 19.907 mph

This is an application of Mean Value Theorem, which states that a function (such as a velocity function) must equal its average value at least once on a closed interval (that is, if the function is continuous and differentiable).

See Math Notes below.