Question

Austin takes 1 minute and 45 seconds to run three-quarters of a circular track. His rate of motion is π/ radians per second.

Answer 1

Length of circular track is:

L = 2*r*pi

He run 3/4 of it so length is:
L' = 3*2/4*r*pi = 3/2*r*pi

To calculate speed of his movement we use formula:
v = s/t where s = L' and t = 1 minute 45 seconds = 105 seconds

v = L'/t = $\frac{3*r*pi}{2*105}$

v = r* pi/70

If we take that r = 1 answer is $\pi /70$