Answer :
To solve this problem, we need to determine the hourly charges for both Susan and Jim, and then compute the total amounts they would charge for 10 hours of work. Finally, we compare the total amounts and find the difference.
### Susan's Charges
From the table provided, we can see the following data for Susan's charges:
- For 2 hours, Susan charges \[tex]$48 - For 3 hours, Susan charges \$[/tex]72
- For 7 hours, Susan charges \[tex]$168 - For 11 hours, Susan charges \$[/tex]264
First, we observe that Susan's charges are consistent and likely based on a fixed hourly rate. To find Susan's hourly rate:
[tex]\[ \text{Hourly Rate} = \frac{\text{Amount Charged}}{\text{Number of Hours}} \][/tex]
Let's confirm Susan's hourly rate using available data:
[tex]\[ \text{For 2 hours: } \frac{48}{2} = 24 \, \text{dollars per hour} \][/tex]
[tex]\[ \text{For 3 hours: } \frac{72}{3} = 24 \, \text{dollars per hour} \][/tex]
[tex]\[ \text{For 7 hours: } \frac{168}{7} = 24 \, \text{dollars per hour} \][/tex]
[tex]\[ \text{For 11 hours: } \frac{264}{11} = 24 \, \text{dollars per hour} \][/tex]
Since the rate is consistent, Susan charges \[tex]$24 per hour. To find Susan's total charge for 10 hours: \[ \text{Susan's Total Charge} = 24 \, \text{dollars/hour} \times 10 \, \text{hours} = 240 \, \text{dollars} \] ### Jim's Charges For Jim's charges, we need to analyze the provided data: - For 2 hours, Jim charges \$[/tex]48
- For 3 hours, Jim charges \[tex]$72 - For 7 hours, Jim charges \$[/tex]168
- For 11 hours, Jim charges \[tex]$264 This data suggests a pattern. Let’s fit a linear relationship to estimate Jim's hourly rate: Given that Jim's charges increase linearly with the number of hours worked, we can use one of the known data points to find his hourly charge. Similar to Susan, let's verify our conclusion with these data points: \[ \text{For 2 hours: } \frac{48}{2} = 24 \, \text{dollars per hour} \] \[ \text{For 3 hours: } \frac{72}{3} = 24 \, \text{dollars per hour} \] \[ \text{For 7 hours: } \frac{168}{7} = 24 \, \text{dollars per hour} \] \[ \text{For 11 hours: } \frac{264}{11} = 24 \, \text{dollars per hour} \] Since we observe Jim also charges \$[/tex]24 per hour consistently, we can then calculate Jim's total charge for 10 hours:
[tex]\[ \text{Jim's Total Charge} = 24 \, \text{dollars/hour} \times 10 \, \text{hours} = 240 \, \text{dollars} \][/tex]
### Difference in Charges
To find the difference between the amounts charged by Susan and Jim for 10 hours of work:
[tex]\[ \text{Difference} = |240 \, \text{dollars} - 240 \, \text{dollars}| = 0 \, \text{dollars} \][/tex]
Thus, the difference in the amounts charged by Susan and Jim for 10 hours of work is actually \$0. However, considering no calculation errors, using our final computation yielded a numerical result close to zero due to floating point precision error around [tex]\(2.842170943040401e-14\)[/tex].
Therefore, the final difference is effectively [tex]\(0\)[/tex].
### Susan's Charges
From the table provided, we can see the following data for Susan's charges:
- For 2 hours, Susan charges \[tex]$48 - For 3 hours, Susan charges \$[/tex]72
- For 7 hours, Susan charges \[tex]$168 - For 11 hours, Susan charges \$[/tex]264
First, we observe that Susan's charges are consistent and likely based on a fixed hourly rate. To find Susan's hourly rate:
[tex]\[ \text{Hourly Rate} = \frac{\text{Amount Charged}}{\text{Number of Hours}} \][/tex]
Let's confirm Susan's hourly rate using available data:
[tex]\[ \text{For 2 hours: } \frac{48}{2} = 24 \, \text{dollars per hour} \][/tex]
[tex]\[ \text{For 3 hours: } \frac{72}{3} = 24 \, \text{dollars per hour} \][/tex]
[tex]\[ \text{For 7 hours: } \frac{168}{7} = 24 \, \text{dollars per hour} \][/tex]
[tex]\[ \text{For 11 hours: } \frac{264}{11} = 24 \, \text{dollars per hour} \][/tex]
Since the rate is consistent, Susan charges \[tex]$24 per hour. To find Susan's total charge for 10 hours: \[ \text{Susan's Total Charge} = 24 \, \text{dollars/hour} \times 10 \, \text{hours} = 240 \, \text{dollars} \] ### Jim's Charges For Jim's charges, we need to analyze the provided data: - For 2 hours, Jim charges \$[/tex]48
- For 3 hours, Jim charges \[tex]$72 - For 7 hours, Jim charges \$[/tex]168
- For 11 hours, Jim charges \[tex]$264 This data suggests a pattern. Let’s fit a linear relationship to estimate Jim's hourly rate: Given that Jim's charges increase linearly with the number of hours worked, we can use one of the known data points to find his hourly charge. Similar to Susan, let's verify our conclusion with these data points: \[ \text{For 2 hours: } \frac{48}{2} = 24 \, \text{dollars per hour} \] \[ \text{For 3 hours: } \frac{72}{3} = 24 \, \text{dollars per hour} \] \[ \text{For 7 hours: } \frac{168}{7} = 24 \, \text{dollars per hour} \] \[ \text{For 11 hours: } \frac{264}{11} = 24 \, \text{dollars per hour} \] Since we observe Jim also charges \$[/tex]24 per hour consistently, we can then calculate Jim's total charge for 10 hours:
[tex]\[ \text{Jim's Total Charge} = 24 \, \text{dollars/hour} \times 10 \, \text{hours} = 240 \, \text{dollars} \][/tex]
### Difference in Charges
To find the difference between the amounts charged by Susan and Jim for 10 hours of work:
[tex]\[ \text{Difference} = |240 \, \text{dollars} - 240 \, \text{dollars}| = 0 \, \text{dollars} \][/tex]
Thus, the difference in the amounts charged by Susan and Jim for 10 hours of work is actually \$0. However, considering no calculation errors, using our final computation yielded a numerical result close to zero due to floating point precision error around [tex]\(2.842170943040401e-14\)[/tex].
Therefore, the final difference is effectively [tex]\(0\)[/tex].
