A student wanted to drive from Austin to San Antonio, 80 miles south of Austin on highway I35. Unfortunately, he entered the highway in the wrong direction and drove all the way to Waco-- 100 miles north of Austin-- before he noticed the error. In Waco, he turned around, drove back to Austin and continued to San Antonio. The whole trip took 3.93 h. What was the student's average speed during this trip? Answer in units of mph. What was the student's average velocity during his trip? Take your positive direction to be southbound on I35. Answer in units of mph.

Average velocity only depends of the final and initial points, in that way the initial point is Austin and the final point is San Antonio, the distance between both cities is 80miles, so average velocity is:

V=x/t, where V is average velocity, x is the distance and t is the time.

V=80mi/3.93h = 20.4mi/h =20.4mph (miles per hour).

Now lets to find Average speed, this is the total distance covered divided between total time spent on it.

[tex]Average speed=\frac{(total distance)}{time} =(\frac{100mi+100mi+80mi}{3.93h}) = \frac{280}{3.93} =71.2mph[/tex]