Let's approach this problem by breaking it down into clear steps:
1. **Understanding the Problem:**
A car starts from a point that is already 22 miles north of a town. It travels further north on a turnpike at a constant speed.
2. **Identifying Known Values:**
- Initial distance from the town: 22 miles
- Car's average speed: 64 miles per hour
- Time spent traveling: 4 hours
3. **Using a Linear Function:**
To solve this problem, we can use a linear function that represents the distance `D` that the car travels in relation to time `t`. A linear function has the form `D = mt + b`, where:
- `D` is the total distance from the town.
- `m` is the rate of change or speed of the car (64 miles per hour in this case).
- `t` is the time spent traveling (4 hours in this case).
- `b` is the initial distance from the town (22 miles in this case).
4. **Setting Up the Function:**
For our specific problem, the linear function will be `D = 64t + 22`.
5. **Calculating Distance Travelled:**
Now, we can plug in the value of time `t` (4 hours) into the function to calculate the total distance from the town after 4 hours:
`D = 64 * 4 + 22`
Let's do the math:
`D = 256 + 22`
`D = 278 miles`
6. **Conclusion:**
Therefore, after 4 hours of traveling on the turnpike, the car is 278 miles north of the town.
