How fast?

Today in class we worked on this warmup problem:
Calculate the average speed if you travel

1. one hour for 10mph and one hour for 20mph


2. one hour for 10mph and two hours for 20mph
   

We discovered that we could not just add (10+20) and divide by 3 hours for the second problem. But that we have to take into consideration the number of hours we traveled at each speed. Someone mentioned that we had to take a "weighted average". Another student mentioned that we had to calculate the "total distance traveled" and divide that by the "total elapsed time ".

Are these three strategies the same? Is one better than the others? Is one easier than the others? Is one more efficient than the others?

We then talked about ways that Ms. Jones and I could grade problem number 3 from HW4. We decided that:

• the total distance traveled has to be 550 miles


• the total elasped time has to be 11 hours

A couple of classes added this requirement as well: "the average speed has to be 50mph"

Do we "need" the last item? Will these items hold true for every valid scenario? Does it hold true for your scenario?