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Marie went golfing and tracked her golf cart's distance from the first hole over time. She stayed at the first hole for the first 30 minutes. Then she drove away from the first hole for the next 2 hours. She stopped to have lunch for 1 hour and then took 2 hours to drive back to the first hole.

Which of the following graphs could represent Marie's situation?
first quadrant of coordinate plane titled Marie's round of golf with the x axis labeled time in hours and the y axis labeled distance in miles, with a line segment from the point 0 comma 0 to one half comma 0, a line segment from one half comma 0 to 2 and a half comma 5, a line segment from 2 and a half comma 5 to 3 and a half comma 5, and a line segment from 3 and a half comma 5 to 5 and a half comma 0
first quadrant of coordinate plane titled Marie's round of golf with the x axis labeled time in hours and the y axis labeled distance in miles, with a line segment from 0 comma 0 to one half comma 0, a line segment from one half comma 0 to 2 and a half comma 5, and a line segment from 2 and a half comma 5 to 4 and a half comma 0
first quadrant of coordinate plane titled Marie's round of golf with the x axis labeled time in hours and the y axis labeled distance in miles, with a segment from the point 0 comma 0 to 2 comma 5, a line segment from 2 comma 5 to 3 comma 5, and a line segment from 3 comma 5 to 5 comma 0
first quadrant of coordinate plane titled Marie's round of golf with the x axis labeled time in hours and the y axis labeled distance in miles, with a line segment from 0 comma 0 to 2 comma 5, and a line segment from 2 comma 5 to 4 comma 0

1 answer

To determine which graph correctly represents Marie's round of golf, we need to break down her activity into segments and analyze how they translate into the graph.

  1. First 30 minutes (0 to 0.5 hours): She is at the first hole, so her distance from the hole is 0 miles. The graph should have a horizontal line segment from (0, 0) to (0.5, 0).

  2. Next 2 hours (0.5 to 2.5 hours): She drives away from the first hole, reaching a distance of 5 miles from the first hole. The distance should increase from 0 to 5 miles, represented by a line segment going from (0.5, 0) to (2.5, 5).

  3. Lunch for 1 hour (2.5 to 3.5 hours): She stays at a distance of 5 miles from the first hole. This should be represented by a horizontal line segment from (2.5, 5) to (3.5, 5).

  4. Returning to the first hole (3.5 to 5.5 hours): She takes 2 hours to drive back to the first hole, which means the distance decreases from 5 miles to 0 miles. This should be represented by a line segment from (3.5, 5) to (5.5, 0).

Now, let's analyze the options given:

  • First option: This graph has a horizontal segment from (0, 0) to (0.5, 0), a segment increasing from (0.5, 0) to (2.5, 5), a horizontal segment from (2.5, 5) to (3.5, 5), and finally a decreasing segment from (3.5, 5) to (5.5, 0). This option correctly represents all segments of Marie's trip.

  • Second option: The graph incorrectly shows the return segment ending at (4.5, 0) instead of (5.5, 0).

  • Third option: The graph presents an incorrect overall time and distance, showing a segment from (0, 0) to (2, 5) instead of accounting for the initial 30 minutes at the hole.

  • Fourth option: Similar to the third option, it fails to accurately represent the lunch step and the return.

Given this analysis, the first option is the graph that best represents Marie's golfing situation.