To solve this problem and create the graph showing Dylan's distance from home over time, we need to break down his trip into segments and plot the distance versus time for each segment.
Let's go through each step of Dylan's journey and compute the cumulative time and the respective distances:
1. Drive to the store:
- Time taken: 2 minutes
- Speed: 5 blocks per minute
- Distance to store: [tex]\(2 \text{ minutes} \times 5 \text{ blocks/minute} = 10 \text{ blocks}\)[/tex]
- Time at this point: 2 minutes
2. Stop at the store:
- Time taken: 6 minutes
- Distance remains 10 blocks
- Cumulative time: [tex]\(2 + 6 = 8\)[/tex] minutes
3. Drive to the bank:
- Speed: 1 block per minute
- Distance from store to bank: 5 blocks
- Time taken: [tex]\(5 \text{ blocks} \div 1 \text{ block/minute} = 5 \text{ minutes}\)[/tex]
- Distance to bank: [tex]\(10 \text{ blocks} + 5 \text{ blocks} = 15 \text{ blocks}\)[/tex]
- Cumulative time: [tex]\(8 + 5 = 13\)[/tex] minutes
4. Stop at the bank:
- Time taken: 7 minutes
- Distance remains 15 blocks
- Cumulative time: [tex]\(13 + 7 = 20\)[/tex] minutes
5. Drive home:
- Speed: 5 blocks per minute
- Distance from bank to home: 15 blocks
- Time taken: [tex]\(15 \text{ blocks} \div 5 \text{ blocks/minute} = 3 \text{ minutes}\)[/tex]
- Cumulative time: [tex]\(20 + 3 = 23\)[/tex] minutes
Now we can plot these points on the graph:
- (0, 0): Dylan starts at home.
- (2, 10): Dylan reaches the store.
- (8, 10): Dylan leaves the store.
- (13, 15): Dylan reaches the bank.
- (20, 15): Dylan leaves the bank.
- (23, 0): Dylan returns home.
Here's the step-by-step solution for the graph:
1. Plot the first point (0, 0).
2. Draw a line from (0, 0) to (2, 10).
3. Draw a horizontal line from (2, 10) to (8, 10).
4. Draw a line from (8, 10) to (13, 15).
5. Draw a horizontal line from (13, 15) to (20, 15).
6. Draw a line from (20, 15) to (23, 0).
This would give you a good visual representation of Dylan's distance from home over time. You can draw this either on graph paper or using a suitable graph plotting tool.
