course MTH 272
resubmitted work
Questions 1-91. If you earn 25.04486 dollars in 5 hours, at what average rate are you earning money, in dollars per hour?
It is difficult to visualize this problem without rounding because our money system isn’t carried out to the hundred-thousandths place. But if we laid out five 5-dollar bills and 5 pennies and said you would get one for every hour you work you would be earning about 5 dollars and 1 penny every hour. Simply said, we would solve this problem 5.05/5
2. If you travel 100.2325 miles in 11 hours, at what average rate are you traveling, in miles per hour?
Assume we are traveling by bike, it is pretty hard to keep a constant rate on a bike. If we traveled 100.2325 miles in 11 hours we would be moving at about 9.11 mph. Its pretty simple to visualize if you look at the big picture. For example, we look at a map and see we traveled the 100 miles from Richmond to Charlottesville in 11 hours, by dividing 100miles/11hrs we would see that we moved at an average rate of 9.11miles/hr
3. If a ball rolling down a grooved track travels 79.70515 centimeters in 6 seconds, at what average rate is the ball moving, in centimeters per second?
Lets say this grooved track comes in sections 10 centimeters in length. If we counted the number of pieces the marble covered in those 6 seconds we would be able to figure out its rate. Our experiment shows that in 6 seconds the marble stops just 1 cm shy of the 8th piece of track. So dividing the 79 cm it traveled by 6 seconds we would conclude its average rate to be about 13 cm/s
4. If you are earning money at the average rate of 57 dollars per hour, how much do you earn in 11 hours?
Lets say for instance you worked all 11 hours in one day for 57 dollars per hour cash, which was paid to you at the end of each hour of completed work. You could stack all the bills and count them at the end of the day. Or you could make 11 piles of 57 dollars and simply multiply 11 x 57 which would equal 627 dollars
5. If you are traveling at an average rate of 37 miles per hour, how far do you travel in 6 hours?
If you are traveling at an average rate of 37 mph you are obviously covering about 37 miles every hour. If you continue that pace for 6 hours you would have traveled 222 miles.
6. If a ball travels at an average rate of 57 centimeters per second, how far does it travel in 6 seconds?
If you can somehow conclude the average rate of the ball is 57 centimeters per second and then let it roll for 6 seconds you would find that the ball would travel approximately 342 centimeters
7. How long does it take to earn 63.13645 dollars at an average rate of 10 dollars per hour?
If you needed to earn 63.13645 dollars and you worked for 10 dollars per hour it would take 6.313645 hours. For to achieve such an accurate response you would have to be paid very quickly so for example instead of 10 dollars per hour you were paid about 16 cents a minute.
8. How long does it take to travel 131.2441 miles at an average rate of 23 miles per hour?
If you are going on a road trip to a destination 131.2441 miles away and you traveled around 23 mph the whole way it would take about 5.71 hours to get there, Because you are covering 23 miles every hour its like subtracting 23 miles from the total distance 5.71 times
9. How long does it take a rolling ball to travel 126.9129 centimeters at an average rate of 21 centimeters per second?
Similar to the last response, by dividing 126.9129cm by 21 cm/s we conclude it would take about 6 seconds to travel this distance. For every second the ball travels 21 cm are subtracted from the total distance
Excellent explanations. You understand this very well.