Answer :
Certainly! Let's go through a step-by-step solution to the problem.
### Step-by-Step Solution:
1. Initial Condition:
The problem states that the number of cars in the parking lot initially is 5 cars.
2. Hourly Changes:
- Cars leaving per hour: 1 car leaves every hour.
- Cars arriving per hour: 3 cars arrive every hour.
3. Net Change Per Hour:
To find the net change in the number of cars per hour, we subtract the number of cars leaving from the number of cars arriving.
[tex]\[ \text{Net change per hour} = \text{Cars arriving per hour} - \text{Cars leaving per hour} \][/tex]
Substituting the given values:
[tex]\[ \text{Net change per hour} = 3 - 1 = 2 \][/tex]
4. Total Change Over Six Hours:
To calculate the total change in the number of cars over six hours, we multiply the net change per hour by the number of hours.
[tex]\[ \text{Total change over 6 hours} = \text{Net change per hour} \times \text{Number of hours} \][/tex]
Substituting the given values:
[tex]\[ \text{Total change over 6 hours} = 2 \times 6 = 12 \][/tex]
5. Final Number of Cars:
To find the final number of cars in the parking lot after six hours, we add the total change over six hours to the initial number of cars.
[tex]\[ \text{Final number of cars} = \text{Initial number of cars} + \text{Total change over 6 hours} \][/tex]
Substituting the given values:
[tex]\[ \text{Final number of cars} = 5 + 12 = 17 \][/tex]
Thus, the detailed solution gives us the following results:
- The net change in the number of cars per hour is 2.
- The total change in the number of cars over six hours is 12.
- The final number of cars in the parking lot after six hours is 17 cars.
### Step-by-Step Solution:
1. Initial Condition:
The problem states that the number of cars in the parking lot initially is 5 cars.
2. Hourly Changes:
- Cars leaving per hour: 1 car leaves every hour.
- Cars arriving per hour: 3 cars arrive every hour.
3. Net Change Per Hour:
To find the net change in the number of cars per hour, we subtract the number of cars leaving from the number of cars arriving.
[tex]\[ \text{Net change per hour} = \text{Cars arriving per hour} - \text{Cars leaving per hour} \][/tex]
Substituting the given values:
[tex]\[ \text{Net change per hour} = 3 - 1 = 2 \][/tex]
4. Total Change Over Six Hours:
To calculate the total change in the number of cars over six hours, we multiply the net change per hour by the number of hours.
[tex]\[ \text{Total change over 6 hours} = \text{Net change per hour} \times \text{Number of hours} \][/tex]
Substituting the given values:
[tex]\[ \text{Total change over 6 hours} = 2 \times 6 = 12 \][/tex]
5. Final Number of Cars:
To find the final number of cars in the parking lot after six hours, we add the total change over six hours to the initial number of cars.
[tex]\[ \text{Final number of cars} = \text{Initial number of cars} + \text{Total change over 6 hours} \][/tex]
Substituting the given values:
[tex]\[ \text{Final number of cars} = 5 + 12 = 17 \][/tex]
Thus, the detailed solution gives us the following results:
- The net change in the number of cars per hour is 2.
- The total change in the number of cars over six hours is 12.
- The final number of cars in the parking lot after six hours is 17 cars.
