Question

Last Monday Craig walked at a constant rate of 3 miles per hour from his home to the bank. He stayed at the bank for 15 minutes, and then jogged home at a constant rate of 6 miles per hour. If the bank is 0.5 mile from his home, which of the following graphs best represents the relationship between Craig's distance from home d, in miles, and time t, in minutes?

1) The graph starts from the origin, moves 2 gridlines to the right and 2 gridlines up to the point with the coordinates 10, 0.50, moves horizontally 3 gridlines to the right to the point with the coordinates 25, 0.50, and then slants one gridline to the right and 2 gridlines down to end at the point on the horizontal axis with the coordinates 30, 0.
2) The graph starts from the origin, moves one gridline to the right and 2 gridlines up to the point with the coordinates 5, 0.50, moves horizontally 3 gridlines to the right to the point with the coordinates 20, 0.50, and then slants 2 gridlines to the right and 2 gridlines down to end at the point on the horizontal axis with the coordinates 30, 0.
3) The graph starts from the origin, moves 2 gridlines to the right and 3 gridlines up to the point with the coordinates 10, 0.75, moves horizontally 3 gridlines to the right to the point with the coordinates 25, 0.75, and then slants one gridline to the right and 3 gridlines down to end at the point on the horizontal axis with the coordinates 30, 0.
4) The graph starts from the origin, moves one gridline to the right and 3 gridlines up to the point with the coordinates 5, 0.75, moves horizontally 3 gridlines to the right to the point with the coordinates 20, 0.75, and then slants 2 gridlines to the right and 3 gridlines down to end at the point on the horizontal axis with the coordinates 30, 0.
5) The graph starts from the origin, moves 2 gridlines to the right and 2 gridlines up to the point with the coordinates 10, 0.50, moves horizontally 2 gridlines to the right to the point with the coordinates 20, 0.50, and then slants 2 gridlines to the right and 2 gridlines down to end at the point on the horizontal axis with the coordinates 30, 0.

Answer 1

The correct graph should start at the origin, move to (10, 0.5) for the walk, remain at (25, 0.5) for the bank stay, and return to the x-axis at (30, 0) for the jog home. Option 1 accurately follows this pattern with the provided coordinates.

Step-by-step explanation:

To determine which graph best represents Craig's distance from home as a function of time, let's analyze the scenario step by step. Craig's walking speed is 3 miles per hour, and the bank is 0.5 mile from his home. If we convert his speed to miles per minute, one hour being 60 minutes, it turns out to be 0.05 miles per minute (3 miles/60 minutes).

Now, the time taken to walk to the bank would be the distance divided by the speed, which is 0.5 mile/(0.05 mile/minute) equaling 10 minutes. Then he stayed at the bank for 15 minutes, making it a total of 25 minutes up to that point. Jogging back at 6 miles per hour, which is 0.1 mile per minute, would take him another 0.5 mile/(0.1 mile/minute) equaling 5 minutes. So, the total time to return home is 30 minutes.

The correct graph should start at the origin (0,0), move right to (10, 0.5) representing the walk to the bank, then a horizontal line to (25, 0.5) for the time spent at the bank, and finally a line back to the x-axis at (30, 0) representing the jog home. This corresponds to a position vs. time graph. Therefore, Option 1 is the correct representation as it follows this pattern accurately with the given coordinates.