A squirrel is running a race where she is on track for her average velocity to be 6.0 m/s. She is distracted by a dummy of an attractive male squirrel and pauses for 3.0 s. As a result her average velocity ends up being 5.0 m/s instead. What is the length of the race? [HINT: construct two equations with the same two unknowns in them and you can solve the system of equations]

90 m

Explanation:

There are two unknowns: the amount of time the squirrel spent running, and the length of the race.  Let's call these t and x, respectively.

The average velocity is the total distance divided by the total time.

5.0 m/s = x / (t + 3.0)

The total distance is the time she spent running times the speed she ran at.

x = (6.0 m/s) t

Substitute and solve:

5 = 6t / (t + 3)

5 (t + 3) = 6t

5t + 15 = 6t

t = 15

She ran for 15 seconds (not including the 3 seconds she stopped).  So the length of the race is:

x = (6.0 m/s) (15 s)

x = 90 m