Question

Alexandra left her house at time zero and drove to the store, which is 9 blocks away, at a speed of 3 blocks per minute. Then she stopped and went into the store for 5 minutes. From there, she drove in the same direction at a speed of 5 blocks per minute until she got to the bank, which is 15 blocks away from the store. She stopped at the bank for 6 minutes. Then she drove home at a speed of 6 blocks every minute. Make a graph of showing the number of blocks away from home that Alexandra is xx minutes after she leaves her house, until she gets back home.

Answer 1

The graph starts at (0,0), a line with slope 3 to (3,9), horizontal line for 5 mins, slope 5 to (18,15), horizontal line for 6 mins, slope -6 back home.

Let's visualize Alexandra's journey on a graph depicting her distance from home over time.

The x-axis will represent time in minutes, and the y-axis will represent the distance in blocks.

At time zero, Alexandra starts at her house, marked as (0, 0) on the graph.

For the first leg of her journey to the store, she travels at a speed of 3 blocks per minute, creating a linear line with a slope of 3.

After 3 minutes, she reaches the store, 9 blocks away, and stays for 5 minutes.

This pause creates a horizontal segment on the graph.

Upon leaving the store, Alexandra drives at a speed of 5 blocks per minute, resulting in a steeper linear line.

After 15 minutes, she arrives at the bank, 15 blocks away, and spends 6 minutes there.

Another horizontal segment represents this stop.

Finally, she heads home at a speed of 6 blocks per minute, forming a line with a slope of 6.

The graph continues until she reaches home, marking the end of her journey.

The graph should show a sequence of linear segments with varying slopes and horizontal segments corresponding to her stops, creating a visual representation of Alexandra's distance from home over time.