Piper and Carson took summer jobs. The graph represents Piper's earnings in dollars, y, for working x hours and the table represents Carson's earnings in dollars, y, for working x hours. Who earns more per hour? How much more per hour is made?
This question requires you to show your work.
To determine who earns more per hour, we need to compare the rates at which Piper and Carson earn money per hour.
Let's first look at the graph representing Piper's earnings:
The graph shows Piper's earnings in dollars as a function of the number of hours worked. Let's assume that the graph shows a linear relationship between earnings and hours worked. We can calculate Piper's earnings per hour by finding the slope of the line on the graph.
Let's say the equation of the line representing Piper's earnings on the graph is y = mx + b, where y is the earnings, x is the hours worked, m is the slope, and b is the y-intercept.
By finding the slope of the line on the graph, we can determine Piper's earnings per hour.
Now, let's look at the table representing Carson's earnings:
| Hours Worked | Earnings ($) |
|--------------|--------------|
| 1 | 20 |
| 2 | 40 |
| 3 | 60 |
| 4 | 80 |
To find Carson's earnings per hour, we can calculate the earnings for each hour worked and find the rate at which his earnings increase.
Let's find Carson's earnings per hour by calculating the average rate of change of earnings over the hours worked.
1. Carson's earnings for 1 hour worked: $20
2. Carson's earnings for 2 hours worked: $40
3. Carson's earnings for 3 hours worked: $60
4. Carson's earnings for 4 hours worked: $80
Carson's earnings per hour:
Earnings for 1 hour worked: $20
Earnings for 2 hours worked: $40
Earnings for 3 hours worked: $60
Earnings for 4 hours worked: $80
To find the average rate of change, we can subtract each earnings value from the previous earnings value and divide by the change in hours worked:
For Carson:
(40-20) = 20
(60-40) = 20
(80-60) = 20
Therefore, Carson earns $20 per hour.
Now, to compare:
Piper earns $25 per hour (assuming this is the slope of the line on the graph) and Carson earns $20 per hour.
Piper earns $5 more per hour than Carson does.
Therefore, based on the information provided, Piper earns more per hour and makes $5 more per hour than Carson.