Question

The Smith family took a road trip from their home in Georgia to Disney world. They drove at a constant rate. When they left their home, they recorded the odometer on their car. After 8 hours of driving, the odometer read 50,832 miles. After 20 hours, the odometer read 51,696 miles.
Determine the mileage on the odometer when the Smith family started their road trip.

Answer 1

To find the mileage on the odometer when the Smith family started their road trip, we can first determine the constant speed at which they were driving.

1. **Calculate the distance traveled in 12 hours** (from 8 hours to 20 hours):
- Odometer reading at 20 hours: 51,696 miles
- Odometer reading at 8 hours: 50,832 miles

\[
\text{Distance traveled} = 51,696 - 50,832 = 864 \text{ miles}
\]

2. **Determine the speed**:
- Time taken to travel this distance = 20 hours - 8 hours = 12 hours
- Speed = Distance / Time

\[
\text{Speed} = \frac{864 \text{ miles}}{12 \text{ hours}} = 72 \text{ miles per hour}
\]

3. **Calculate the distance traveled in the first 8 hours**:
\[
\text{Distance in 8 hours} = \text{Speed} \times \text{Time} = 72 \text{ miles/hour} \times 8 \text{ hours} = 576 \text{ miles}
\]

4. **Find the initial mileage**:
- Odometer reading after 8 hours was 50,832 miles.
- Therefore, the initial mileage can be calculated as follows:

\[
\text{Initial mileage} = \text{Odometer after 8 hours} - \text{Distance traveled in first 8 hours}
\]

\[
\text{Initial mileage} = 50,832 - 576 = 50,256 \text{ miles}
\]

Thus, the mileage on the odometer when the Smith family started their road trip was **50,256 miles**.