SL2RL-Math247

12 May 2009

Thinking questions for rates

Filed under: 8-12,algebra,education,math — admin @ 11:01 am

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

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).

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