Rutgers/Lucent ALLIES IN TEACHING MATHEMATICS AND TECHNOLOGY Grant
Using technology not simply to do things better, but to do better things.


INCORRECT STUDENT RESPONSES:
A Day At The Races


Answer #1: The average speed is 75 mph.
Explanation: In order to do this problem you must first know the rules for finding averages. The rules are as follows:
  1. add up all of the numbers given
  2. divide the answer you get in step 1 by the amount of numbers you added up together
  3. the resulting number is your average
I got two numbers for this problems and they are 60mph and 90mph. I followed the steps.
  1. 60+90=150
  2. 150/2=75
  3. The average for these two speeds is 75 mph.
BONUS: The speed in the second lap is 90 mph. For the bonus I was given the speed of the first lap, 30mph and the average resultant of the first and second lap, 60mph. The steps to find the speed are:
  1. multiply the average by the amount of numbers that you are supposed to have
  2. subtract the number that you are orignally given from your answer in step 1
  3. add the numbers from step 2 and the the orginal number given together
  4. to test your answer, divide your total from step 3 by the amount of numbers you were supposed to have
I did the following steps in order to find the speed for the second lap:
  1. 60*2=120
  2. 120-30=90 mph
  3. 90+30=120
  4. 120/2=60 mph
The speed for the the second lap is 90 mph in order for you to get an average of 60 mph from a beginning speed of 30 mph.


Answer #2: The average speed of the motorcycle for the two laps together was 18.5 miles per hour.

Explanation: I took it like this: When you run around a gym four times (4 laps) you complete one mile. So, if he's runs that one lap then he's not going the whole mile. Therefore, I broke the lap into four (4 laps = 1 mile). So what I did was this: 5280/4=1320, 1320/60=22 mi, 1320/90=14.6 mi, then I added 14.6mi + 22mi. = 36.6, and finally I devided 36.6/2 to get the average.


Answer#3: The average speed is 2700 miles.
Explanation: Ok let me start off by saying that we know that when he was practicing he was racing 60 miles per hour but then when he was doing the actual race he was racing 90 miles per hour. Then we know he raced 2 different laps. Ok so to find this answer what I did was multiply 60 and 90. 6x9=54 plus add the 2 zeros since 0x0=0 and theres 2 zero's in the problem. So the answer totals up to 5400. However, we have to take in consideration that they ran 2 different laps so we have to divide 2 by 5400 to find the total. 2 divided by 54 is 27 and again there are 2 zero's in 5400 so we have to add them to the 27. This gives me a total of 2700 and thats the average speed they rode.


Answer #4: The average speed is 48mph.
Explanation: To solve this problem, I broke down the mph into miles per minute, then I added them together and then converted that back to miles per hour.
I started out by breaking down the 60mph. I knew that that meant that he traveled 60 miles in 60 minutes which meant that he traveled one mile every minute.
I then broke down the 90mph. I knew that that meant that for every 60 minutes, he traveled 90 miles which means that for every mile, it takes him one minute and 30 seconds to complete it.
I then added both 'proportions' [(1 mile/1 minute)+(1 mile/1.5 minutes)] and that gave me an average of 2 miles for every 2.5 miles. I divided 2.5 by 60 to see how many "2.5 intervals" there are in an hour and it's 24. I then multiplied the 2 miles by 24 to get how many miles it is per hour. That gave me the answer of 48 miles per hour.


Answer #5: The average is 60 mph.
Explanation: In one practice lap he ran 60 mph. 60 miles/60 mintues.
In the 2nd lap he ran 90 mph. 90 miles/ 60 mintues.
To find the average you have to add the two and divide them by the amount.
60/60 + 90/60 = 150/60 =2.5 With this 2.5 you use and divide with the 150 miles. 150/2.5= 60 miles per hour


Answer #6: The answer to the question is 75mph and for the bonus it's 90mph
Explanation: In order to arrive at my answer for the problem i decided to add the two different speeds together and divide them by two because that's how u find the average of anything (the majority of the time) This is the only way i could think of to solve the problem.
(60mph + 90mph)/2 = 75mph
For bonus i saw that 60+60/2 would give me an average of 60mph and that 60+60=120. But i also saw that the 1st lap was already run at 30mph so i subtractred 120-30 which gave me 90mph And to check myself, (90+30)/2=60mph

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