Question
It takes Mike 1/2 hour to walk 2 miles he start walking in his spare time, but because he wants to make sure he’s not done going to desire this, and he created a data table at which ratio for the constant of proportionality appear
Answers
GPT-4o mini
To analyze Mike's walking rate, we establish a ratio based on the information provided.
Mike walks 2 miles in 1/2 hour. To find his walking speed in miles per hour (mph), we can use the following ratio:
- **Distance:** 2 miles
- **Time:** 1/2 hour
To find the rate (miles per hour), we will convert the time to hours:
1. **Convert time to hours:**
\[
\frac{1}{2} \text{ hour} = 0.5 \text{ hours}
\]
2. **Calculate the speed:**
\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{2 \text{ miles}}{0.5 \text{ hours}} = 4 \text{ miles per hour}
\]
The constant of proportionality (the ratio of miles to hours) here is 4, which means for every hour Mike walks, he covers 4 miles.
To create a data table that shows this constant of proportionality, we can list different distances and corresponding times:
| Distance (miles) | Time (hours) |
|------------------|--------------|
| 2 | 0.5 |
| 4 | 1 |
| 6 | 1.5 |
| 8 | 2 |
| 10 | 2.5 |
From this table, we can see that the ratio of distance to time remains constant at 4 miles per hour, confirming that Mike's walking speed is consistent.
Mike walks 2 miles in 1/2 hour. To find his walking speed in miles per hour (mph), we can use the following ratio:
- **Distance:** 2 miles
- **Time:** 1/2 hour
To find the rate (miles per hour), we will convert the time to hours:
1. **Convert time to hours:**
\[
\frac{1}{2} \text{ hour} = 0.5 \text{ hours}
\]
2. **Calculate the speed:**
\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{2 \text{ miles}}{0.5 \text{ hours}} = 4 \text{ miles per hour}
\]
The constant of proportionality (the ratio of miles to hours) here is 4, which means for every hour Mike walks, he covers 4 miles.
To create a data table that shows this constant of proportionality, we can list different distances and corresponding times:
| Distance (miles) | Time (hours) |
|------------------|--------------|
| 2 | 0.5 |
| 4 | 1 |
| 6 | 1.5 |
| 8 | 2 |
| 10 | 2.5 |
From this table, we can see that the ratio of distance to time remains constant at 4 miles per hour, confirming that Mike's walking speed is consistent.