course phy 121
Question: If you make $50 in 5 hr, then at what rate are you earning money?
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Your solution:
50/5 =10
$10 per hour
confidence rating #$&*: ok
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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:
60,000/12= 5000
$ 5000 per month
confidence rating #$&*: ok
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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?
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Your solution:
An average of $5000 per month
confidence rating #$&* ok
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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?
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Your solution:
300/6= 50 miles/hour
confidence rating #$&*: ok
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Self-critique (if necessary): ok
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Question: `q006. If you use 60 gallons of gasoline on a 1200 mile trip, then at what average rate are you using gasoline, with respect to miles traveled?
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Your solution:
60/1200=.05 gallons/mile
confidence rating #$&* ok
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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:
The word 'average' in the context of the dollars / month, miles / gallon types of questions we have been answering was used because we expect that in different months different amounts were earned, or that over different parts of the trip the gas mileage might have varied, but that if we knew all the individual quantities (e.g., the dollars earned each month, the number of gallons used with each mile) and averaged them in the usual manner, we would get the .05 gallons / mile, or the $5000 / month. In a sense we have already added up all the dollars earned in each month, or the miles traveled on each gallon, and we have obtained the total $60,000 or 1200 miles. Thus when we divide by the number of months or the number of gallons, we are in fact calculating an average rate.
confidence rating #$&*: ok
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Self-critique (if necessary): ok
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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?
Your solution:
15/40= .375pounds/ pushup
confidence rating #$&*: ok
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Question: `q009. In another part of the study, participants all did 30 pushups per day, but one group did pushups with a 10-pound weight on their shoulders while the other used a 30-pound weight. At the end of the study, the first group had an average lifting strength of 171 pounds, while the second had an average lifting strength of 188 pounds. At what average rate did lifting strength increase with respect to the added shoulder weight?
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Your solution:
17/20=8.5 lifting pounds
confidence rating #$&*: ok
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Self-critique (if necessary): ok
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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:
100/10= 10 meters
confidence rating #$&* ok
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Question: `q011. During a race, a runner passes the 100-meter mark moving at 10 meters / second, and the 200-meter mark moving at 9 meters / second. What is your best estimate of how long it takes the runner to cover the 100 meter distance?
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Your solution:
(10 m/s + 9 m/s ) / 2 = 9.5 m/s.
(100 meters) / (9.5 m/s) = 10.5 sec, approx
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Question: `q012. We just averaged two quantities, adding them and dividing by 2, to find an average rate. We didn't do that before. Why we do it now?
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Your solution:
In previous examples the quantities weren't rates. We were given the amount of change of some accumulating quantity, and the change in time or in some other quantity on which the first was dependent (e.g., dollars and months, miles and gallons). Here we are given 2 rates, 10 m/s and 9 m/s, in a situation where we need an average rate in order to answer a question. Within this context, averaging the 2 rates was an appropriate tactic.
confidence rating #$&* ok
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Self-critique (if necessary): ok
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