Question

Aiden left his house at time zero and drove for 4 minutes to the store, at a speed of 2 blocks per minute. Then he stopped and went into the store for 7 minutes. From there, he drove in the same direction at a speed of 6 blocks per minute until he got to the bank, which is 12 blocks away from the store. He stopped at the bank for 2 minutes. Then he drove home at a speed of 5 blocks every minute.

Make a graph showing the number of blocks away from home that Aiden is xx minutes after he leaves his house until he gets back home.

Answer 1

Aiden's position at different time intervals can be calculated and plotted on a graph. His position is 0 blocks away from home initially, then 8 blocks away after 4 minutes, 20 blocks away after 13 minutes, and remains at 20 blocks until 15 minutes. After 15 minutes, his position will be negative as he is on the way back home.

Step-by-step explanation:

To create a graph showing the number of blocks away from home that Aiden is at a given time, we need to determine his position at different time intervals. Let's break down his journey and calculate his position for each segment:

1. From home to the store: Aiden drives for 4 minutes at a speed of 2 blocks per minute. So, after 4 minutes, he would be 2 * 4 = 8 blocks away from home.
2. At the store: Aiden stops and spends 7 minutes inside the store. His position remains the same during this time, so he is still 8 blocks away from home.
3. From the store to the bank: Aiden drives at a speed of 6 blocks per minute for a distance of 12 blocks. Therefore, the time taken to reach the bank is 12 / 6 = 2 minutes. During this time, Aiden's position changes from 8 blocks to 8 + 6 * 2 = 20 blocks away from home.
4. At the bank: Aiden stops for 2 minutes at the bank. His position remains the same, so he is still 20 blocks away from home.
5. From the bank to home: Aiden drives at a speed of 5 blocks per minute. To calculate the time it takes to reach home, we can subtract the time spent on the previous segments from the total time: 4 + 7 + 2 + 2 = 15 minutes. Therefore, he will be 20 - 5 * 15 = -55 blocks away from home at this time.

Based on these calculations, we have the following positions at different time intervals:
0 minutes: 0 blocks away from home (starting point)
4 minutes: 8 blocks away from home
11 minutes: 8 blocks away from home
13 minutes: 20 blocks away from home
15 minutes: 20 blocks away from home
For times greater than 15 minutes, Aiden is on his way back home, so his position will be negative.

Using this information, we can plot a graph with time on the x-axis and the number of blocks away from home on the y-axis. The graph will consist of a flat line at 0 blocks until 4 minutes, then a horizontal line at 8 blocks until 11 minutes, followed by another horizontal line at 20 blocks until 15 minutes, and finally, a decreasing line with a negative slope after 15 minutes.