course Mth 271
001. Rates*********************************************
Question: If you make $50 in 5 hr, then at what rate are you earning money?
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Your solution:
50 = 5x
x = 10
Confidence Assessment:
Great
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Self-critique (if necessary):
Great
Self-critique Rating:
To find the answer to this question, I had to construct a simple equation and solve for x.
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Question: `q003.If you make $60,000 per year then how much do you make per month?
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Your solution:
60000 = 12x
x = 5000
Confidence Assessment:
Great
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Self-critique (if necessary):
OK
Self-critique Rating:
To find the solution to this problem, I constructed a simple equation and solved for x.
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Question: `q004. Suppose that the $60,000 is made in a year by a small business. Would be more appropriate to say that the business makes $5000 per month, or that the business makes an average of $5000 per month?
Your solution:
A small business is different than a person. Where a person generally has a set income (depending on the presence of absence of raises, bonuses, and/or compensation), but a small business has an ever changing income.
Confidence Assessment:
Great
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Self-critique (if necessary):
OK
Self-critique Rating:
This was a simple logic problem, I feel confident about my logic skills.
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Question: `q005. If you travel 300 miles in 6 hours, at what average rate are you covering distance, and why do we say average rate instead of just plain rate?
Your solution:
300 = 6x
x = 50
Confidence Assessment:
Great
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Self-critique (if necessary):
Great
Self-critique Rating:
To solve this problem, I constructed a simple equation and solved for x.
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Question: `q006. If you use 60 gallons of gasoline on a 1200 mile trip, then at what average rate are you using gasoline, with respect to miles traveled?
Your solution:
60 = 1200x
x = .05
Confidence Assessment:
Great
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Self-critique (if necessary):
OK
Self-critique Rating:
To solve this problem, I constructed a simple equation and solved for x.
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Question: `q007. The word 'average' generally connotes something like adding two quantities and dividing by 2, or adding several quantities and dividing by the number of quantities we added. Why is it that we are calculating average rates but we aren't adding anything?
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Your solution:
As in the preceding question, it has been assumed that each mile used the same amount of gas, but this most likely isnt the case. The total amount of gas (60 gallons) per distance (1200 miles) is an addition of each gallon per mile. To find the assumed amount of gas per mile, we take the average.
Confidence Assessment:
OK
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Self-critique (if necessary):
OK
Self-critique Rating:
My reasoning to my answer is clearly outlined in the solution. See above.
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Question: `q008. In a study of how lifting strength is influenced by various ways of training, a study group was divided into 2 subgroups of equally matched individuals. The first group did 10 pushups per day for a year and the second group did 50 pushups per day for year. At the end of the year to lifting strength of the first group averaged 147 pounds, while that of the second group averaged 162 pounds. At what average rate did lifting strength increase per daily pushup
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Your solution:
10 50 = 40 pushups
147 162 = 15 pounds
40x = 15
x = 15/40
x = .375
Confidence Assessment:
OK
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Self-critique (if necessary):
I had to read through the solution to understand what the question was asking of me.
Self-critique Rating:
To find the answer, I had to take the weight and number of pushups of the control group and compare it to the test group. This gave me the percent increase.
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Question: `q009. In another part of the study, participants all did 30 pushups per day, but one group did pushups with a 10-pound weight on their shoulders while the other used a 30-pound weight. At the end of the study, the first group had an average lifting strength of 171 pounds, while the second had an average lifting strength of 188 pounds. At what average rate did lifting strength increase with respect to the added shoulder weight?
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Your solution:
30 10 = 20 pounds
188 171 = 17 pounds
17 = 20x
x = 17/20
x = .85
Confidence Assessment:
OK
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Self-critique (if necessary):
OK
Self-critique Rating:
To find the answer, I had to take the add weight and weight increase of the control group and compare it to the test group. This gave me the percent increase.
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Question: `q010. During a race, a runner passes the 100-meter mark 12 seconds after the start and the 200-meter mark 22 seconds after the start. At what average rate was the runner covering distance between those two positions?
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Your solution:
200 100 = 100 meters
22 12 = 10 seconds
X = 100 meters/10 seconds = 10 m/s
Confidence Assessment:
OK
Self-critique (if necessary):
OK
Self-critique Rating:
To find the answer, I simply repeated the same processes as the two preceding equations.
Question: `q011. During a race, a runner passes the 100-meter mark moving at 10 meters / second, and the 200-meter mark moving at 9 meters / second. What is your best estimate of how long it takes the runner to cover the 100 meter distance?
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Your solution:
200 100 = 100 meters
10 m/s + 9 m/s = 19 m/s
19/2 = 9.5 m/s
100 meters/9.5 m/s = 10.5 s
Confidence Assessment:
OK
Self-critique (if necessary):
OK
Self-critique Rating:
To find the answer to this solution, I had to find how many seconds it would take the runner to run one meter. Once I found that answer, I could determine how long it would take the runner to run 100 meters.
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Question: `q012. We just averaged two quantities, adding them in dividing by 2, to find an average rate. We didn't do that before. Why we do it now?
Your solution:
We did this now because the rate was changing. Before we were given a set measurement, not a fluctuating rate of change.
Confidence Assessment:
OK
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Self-critique (if necessary):
OK
Self-critique Rating:
This was a logic question, I feel very confident about my logic skills.
Very good work.
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