Let’s suppose you are working on problems involving distance, speed and time. You might consider posing these problems one at a time.

**Q1:** Suppose I travel 2 hours at 40 mph and then 2 hours at 20 mph. What is my average speed for the trip?

**Q2:** Suppose I travel 2 hours at 40 mph and then 4 hours at 20 mph. What is my average speed for the trip?

**Q3:** Suppose the cities Abat and Boto are 80 miles apart and I travel from Abat to Boto at 40 mph and from Boto to Abat at 20 mph. What is my average speed for the trip?

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I should point out that I am now a units freak since my engineering husband always insisted that I include units when talking to him. In becoming such, I have learn to avoid many traps such as answering 30 mph to Q3.

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Average speed = total distance/total time. Notice that the unit is correct!

**A1: ** The total distance is: 2 hrs*40 mph+2 hrs*20 mph= 120 miles. The total time is: 2 hrs+2 hrs=4 hrs.

average speed = 120 miles/4hrs = **30 mph**

**A2: ** The total distance is: 2 hrs*40 mph+4 hrs*20 mph= 160 miles. The total time is: 2 hrs+4 hrs = 6 hrs.

average speed = 160 miles/6 hrs **= 26.7 mph**

**A3: ** The total distance is: 80 miles+80 miles=160 miles.

The total time must be calculated and is: 80 miles/40 mph + 80 miles/20 mph =2 hrs+4 hrs=6 hrs.

So this is the same problem as Q2. I drive twice as long a time coming back at 20 mph as going at 40 mph .

average speed = **26.7 mph**

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**Resource: **These questions arose when I was thinking about the 2nd comment to my last blog about **harmonic averages** (thank-you Math Maker!) and so I looked around for more information at wikipedia (more about this to come in future blogs).