You have already traveled 30 miles east and then 30 miles north. To get back to the start, you travel 30 miles west in 1 hour and then 30 miles south in a half hour. What are your average speed and average velocity for the whole rally? Explain your answer.

We can calculate the average speed for the last two steps only since timing is provided at those stages only. 
Speed at the third step: [tex] \frac{30}{1}=30m/h [/tex]
Speed at the fourth step: [tex] \frac{30}{0.5h} =60miles/h[/tex]
The average speed then:
[tex] \frac{30+60}{2}=45miles/h [/tex]