Bethany drove 70 miles to her sister's house. The graph shows the first part of her journey and her stop at a service station. After the stop, she continued at a steady speed and reached her sister's house at 12:30. We need to determine which of the lines A-D completes the distance-time graph of Bethany's journey.

1. Problem Description

Bethany drove 70 miles to her sister's house. The graph shows the first part of her journey and her stop at a service station. After the stop, she continued at a steady speed and reached her sister's house at 12:

3

0. We need to determine which of the lines A-D completes the distance-time graph of Bethany's journey.

2. Solution Steps

First, we need to identify the time Bethany resumed driving after her stop. From the graph, the stop ends at 12:

0

0. She reached her destination at 12:

3

0. So, the total time of the last leg of the trip is 30 minutes (12:30 - 12:00).

Next, we need to find the distance she had already traveled before the stop. From the graph, she had traveled 40 miles before the stop.

The remaining distance to her sister's house is $70 - 40 = 30$ miles.

Now we need to find the line that shows her traveling 30 miles in 30 minutes.

Line A ends near 80 miles well above the 70 miles she had to travel. Line A is incorrect.

Line B ends near 73 miles well above the 70 miles she had to travel. Line B is incorrect.

Line C ends at 70 miles. Line C shows Bethany arriving at her sister's house at 12:

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0. Line D stays at 40 miles, indicating that she did not move.

3. Final Answer

C