course MTH 272
1. If you earn 154.9823 dollars in 11 hours, at what average rate are you earning money, in dollars per hour?
To get the average rate, in dollars per hour, of earned money we could represent the number 154.9823 physically, dividing it into 11 groups. However, the simplest way is to divide the number 154.9823, the total amount of money earned, by the number 11, the number of hours worked.
So 154.9823 dollars divided by 11 dollars would give us the average rate of earning money in dollars per hour. 154.9823 dollars/ 11 hours= 14.0893 dollars per hour.
2. If you travel 116.9053 miles in 9 hours, at what average rate are you traveling, in miles per hour?
We could physically partition out the distance of 116.9053 miles into 9 groups, representing the 9 hours traveled, to get the average rate of travel. Division with the numbers 116.9053 miles and 9 hours is much easier.
The average rate of travel can be found by dividing the number of miles traveled, 116.9053, by the number of hours traveled, 9. So 116.9053 miles/9 hours = 12.9895 miles per hour.
3. If a ball rolling down a grooved track travels 48.73081 centimeters in 9 seconds, at what average rate is the ball moving, in centimeters per second?
To get the average rate of movement in centimeters per second, we could physically represent the distance of 48.73081 centimeters and divide it into 9 groups, which would recreate the 9 seconds traveled on the track. The simplest way to solve this problem is by numerical division.
So the 48.73081 centimeters divided by 9 seconds would give us the average rate the ball is moving, in centimeters per second. 48.73081 centimeters/ 9 seconds = 4.85978 centimeters per second.
4. If you are earning money at the average rate of 66 dollars per hour, how much do you earn in 8 hours?
Because you are earning 66 dollars in 1 hour, we could bring together 8 groups of 66 dollars to physically represent the amount of money you will earn in 8 hours. The simplest way to attain this figure would be to use numerical multiplication.
To find out how much money you will earn in 8 hours, we need to multiply 8 hours by 66 dollars per hour. So 8 hours * 66 dollars/hour = 528 dollars.
5. If you are traveling at an average rate of 75 miles per hour, how far do you travel in 6 hours?
Because you are traveling 75 miles per hour in 1 hour, we could physically represent the distance traveled in 6 hours by arranging six groups of 75 to get a total. A much easier method is to use numerical multiplication.
75 miles per hour multiplied by the number of hours traveled, 6, would give us the total distance traveled in 6 hours. 75 miles/hour * 6 hours = 450 miles.
6. If a ball travels at an average rate of 42 centimeters per second, how far does it travel in 10 seconds?
Because in 1 second a ball travels 42 centimeters, we could physically total the distance traveled in 10 seconds by collecting 10 groups of 420. However, numerical multiplication is much simpler for solving this problem.
If a ball travels 42 centimeters in 1 second, then a ball traveling for 10 seconds would yield a distance equivalent to 42 centimeters per second multiplied by 10 seconds. So 42 centimeters/second * 10 = 420 centimeters.
7. How long does it take to earn 183.9925 dollars at an average rate of 21 dollars per hour?
To reach the amount of 183.9925 dollars, we could multiply the average amount of 21 dollars per hour by increasing amounts of hours until we got to 183.9925 dollars. A much easier method would be to set up an equation.
If on average 21 dollars per hour is earned, we could figure out how long it takes to earn 183.9925 dollars by setting up a simple equation and using the principles of numerical multiplication and division. Because we need to know how many hours (h) are needed to reach 183.9925 dollars, we could set h multiplied by 21 dollars per hour equal to 183.9925 dollars. So 21h = 183.9925.
To solve the problem, we can divide 183.9925 dollars by the 21 dollar/hour average. So 183.9925 dollars/ 21 dollars/hour =8.7615 hours.
8. How long does it take to travel 98.46438 miles at an average rate of 15 miles per hour?
Although we could collect increasing amounts of groups of 15 until we reached 98.46438 miles, it is much simpler to use numerical multiplication and division to figure out how long it takes to travel 98.46438 miles at 15 miles per hour.
We can set up an easy equation to solve the problem. Because we are solving for the number of hours (h) it takes to travel 98.46438 miles, we could set h times the average 15 miles per hour equal to 98.46438 miles. So 15h = 98.46438 miles.
To solve the equation, we need to divide 98.46438 miles by 15 miles per hour. So 98.46438 miles/ 15 miles/hour = 6.56429 hours.
9. How long does it take a rolling ball to travel 26.29359 centimeters at an average rate of 7 centimeters per second?
We could collect increasing groups of 7 centimeters until we reached 26.29359 centimeters to figure out the number of seconds needed to reach 26.29359 centimeters. But an easier method would be to set up and equation that utilizes multiplication and division principles.
Because we are trying to find the number of seconds (s) it would take to travel 26.29359 centimeters at a rate of 7 centimeters per second, we could set s times the average of 7 centimeters per second equal to 26.29359 centimeters. So 7s = 26.29359.
To find out how long it takes for the ball to travel, we need to divide 26.29359 centimeters by 7 centimeters per second to get s. So 26.29359 centimeters/ 7 centimeters/second = 3.7562 seconds.
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