Answer :
Sure! Let's go through the situations one by one to see which match the equation [tex]\(500 = 100x\)[/tex].
### Situation 1:
An object travels 500 feet for 100 seconds.
We can express this situation using the formula for distance:
[tex]\[ \text{distance} = \text{rate} \times \text{time} \][/tex]
In this case:
- The distance is 500 feet.
- The time is 100 seconds.
- The rate would be calculated as [tex]\( \frac{500 \text{ feet}}{100 \text{ seconds}} = 5 \text{ feet per second} \)[/tex].
Thus, this situation can be described by the equation [tex]\( 500 = 100 \times 5 \)[/tex], so it fits because the rate (5 feet per second) is what makes the equation true.
### Situation 2:
An object travels 500 miles at a rate of 100 miles per hour.
Here, we use the formula again:
[tex]\[ \text{distance} = \text{rate} \times \text{time} \][/tex]
In this case:
- The distance is 500 miles.
- The rate is 100 miles per hour.
- The time can be found by rearranging the formula to [tex]\( \text{time} = \frac{\text{distance}}{\text{rate}} = \frac{500 \text{ miles}}{100 \text{ miles per hour}} = 5 \text{ hours} \)[/tex].
So, the equation [tex]\( 500 = 100 \times 5 \)[/tex] holds true because the time (5 hours) is what makes the equation valid.
### Situation 3:
An object travels at 500 miles per hour for 100 hours.
We use the same formula:
[tex]\[ \text{distance} = \text{rate} \times \text{time} \][/tex]
Here:
- The rate is 500 miles per hour.
- The time is 100 hours.
- Thus, the distance is [tex]\( 500 \text{ miles per hour} \times 100 \text{ hours} = 50,000 \text{ miles} \)[/tex].
This situation does not fit [tex]\(500 = 100x\)[/tex] because the numbers produce a much larger distance (50,000) compared to 500.
### Situation 4:
An object travels 100 inches per minute for 500 minutes.
Using the formula again:
[tex]\[ \text{distance} = \text{rate} \times \text{time} \][/tex]
In this case:
- The rate is 100 inches per minute.
- The time is 500 minutes.
- The total distance is [tex]\( 100 \text{ inches per minute} \times 500 \text{ minutes} = 50,000 \text{ inches} \)[/tex].
This situation does not fit [tex]\(500 = 100x\)[/tex] either as it results in a total distance of 50,000 inches.
Therefore, the situations that match the formula [tex]\(500 = 100x\)[/tex] are Situation 1 and Situation 2.
### Situation 1:
An object travels 500 feet for 100 seconds.
We can express this situation using the formula for distance:
[tex]\[ \text{distance} = \text{rate} \times \text{time} \][/tex]
In this case:
- The distance is 500 feet.
- The time is 100 seconds.
- The rate would be calculated as [tex]\( \frac{500 \text{ feet}}{100 \text{ seconds}} = 5 \text{ feet per second} \)[/tex].
Thus, this situation can be described by the equation [tex]\( 500 = 100 \times 5 \)[/tex], so it fits because the rate (5 feet per second) is what makes the equation true.
### Situation 2:
An object travels 500 miles at a rate of 100 miles per hour.
Here, we use the formula again:
[tex]\[ \text{distance} = \text{rate} \times \text{time} \][/tex]
In this case:
- The distance is 500 miles.
- The rate is 100 miles per hour.
- The time can be found by rearranging the formula to [tex]\( \text{time} = \frac{\text{distance}}{\text{rate}} = \frac{500 \text{ miles}}{100 \text{ miles per hour}} = 5 \text{ hours} \)[/tex].
So, the equation [tex]\( 500 = 100 \times 5 \)[/tex] holds true because the time (5 hours) is what makes the equation valid.
### Situation 3:
An object travels at 500 miles per hour for 100 hours.
We use the same formula:
[tex]\[ \text{distance} = \text{rate} \times \text{time} \][/tex]
Here:
- The rate is 500 miles per hour.
- The time is 100 hours.
- Thus, the distance is [tex]\( 500 \text{ miles per hour} \times 100 \text{ hours} = 50,000 \text{ miles} \)[/tex].
This situation does not fit [tex]\(500 = 100x\)[/tex] because the numbers produce a much larger distance (50,000) compared to 500.
### Situation 4:
An object travels 100 inches per minute for 500 minutes.
Using the formula again:
[tex]\[ \text{distance} = \text{rate} \times \text{time} \][/tex]
In this case:
- The rate is 100 inches per minute.
- The time is 500 minutes.
- The total distance is [tex]\( 100 \text{ inches per minute} \times 500 \text{ minutes} = 50,000 \text{ inches} \)[/tex].
This situation does not fit [tex]\(500 = 100x\)[/tex] either as it results in a total distance of 50,000 inches.
Therefore, the situations that match the formula [tex]\(500 = 100x\)[/tex] are Situation 1 and Situation 2.
