Rates

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course Math 158

Submitted August 30, 2010 @ 8:40pm - Rates

Question: If you make $50 in 5 hr, then at what rate are you earning money?YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

When you divide 50 (amount earned) by 5(hrs worked) you get 10 per hour which is the rate you earn money.

confidence rating #$&*

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3

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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:

When you divide $60,000 (annual earnings) by number of months in a year (12) you get $5,000 which is the amount earned per month.

confidence rating #$&*

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3

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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:

It would be more appropriate to say that a business makes an average of $5,000 per month because the profits or the expenses for the business may vary each month.

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3

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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:

If you divide 300(miles traveled) by 6(hrs of travel) you get an average of 50 miles traveled per hour. You would refer to this a an average rate because of uncontrollable circumstances, such as traffic, weather, conditions of the road, etc.

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3

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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:

Dividing 1200 miles by 60 gallons of gas, you get 20 miles per gallon.

confidence rating #$&*

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3

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Self-critique (if necessary):

I fell into a routine of answering questions and did no pay attention to what the question was asking of me. I should have divided 60 gallons of gas by the 1200 miles to get .05 miles per gallon of gas. I understand how you would get this answer I just need to be more careful in reading the question.

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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:

If we knew all the specific data regarding the gallons of gas, miles traveled, or money earned, etc. you would use this method but since uncontrollable circumstances come into each situation, however, in these problems we are assuming that the average has already been calculated in the numbers we are given.

confidence rating #$&*

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3

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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:

The second group perform 40 more pushups per day than the first group with an average of 15 more pounds.

confidence rating #$&*

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2

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Self-critique (if necessary):

I could easily see the difference in the quantity of pushups per day and average lifting of each group but wasn’t sure how to proceed after getting this data. I was a little confused by the wording of the question.

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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=20lb difference and 188-171 = 17lb difference in lifting strength. So you divide 17lb lifting strength by 20lb weight difference which = .85 lifting pounds of added weight.

confidence rating #$&*:

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3

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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 distance and 22-12 = 10 seconds. So they traveled 100 meters in 10 seconds and if you divide 100/10 you get 10 meters traveled per second.

confidence rating #$&*:

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3

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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 intervening 100 meter distance?

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Your solution:

During the first 100 meters, they ran 10 meters per second and the second 100 meters they ran 9 meters per second. A best estimate would be to add 10 + 9 = 19 and divide by 2 = 9.5 meters. So to run an additional 100 meters/9.5 = 10.5 seconds It would take an estimated 10.5 seconds to run an additional 100 meters.

confidence rating #$&*

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3

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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 the previous questions, all the details were given but there was an assumed average. In this question not all the details were given either because you weren’t sure if the runner’s pace would continue to slow down so the only way knew to attempt the problem was to average to two speeds and then divide the distance by this average.

confidence rating #$&*

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2

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Self-critique (if necessary):

As my solution indicated. I wasn’t sure of how to get this answer but I wanted to try to get an answer, so I decided to average the two speeds because it stated “your best estimate” in the question.

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