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Answer :
Let's break down each situation to determine which matches the formula [tex]\(500 = 100x\)[/tex].
1. An object travels at 500 miles per hour for 100 hours.
- The formula suggests finding [tex]\(x\)[/tex] such that [tex]\(500 = 100 \times x\)[/tex].
- In this scenario, the distance the object would cover is:
[tex]\[
\text{Distance} = \text{Speed} \times \text{Time} = 500 \text{ miles/hour} \times 100 \text{ hours} = 50000 \text{ miles}
\][/tex]
- This does not match the formula [tex]\(500 = 100x\)[/tex].
2. An object travels 500 diret for 100 seconds.
- The term 'diret' is unclear, but assuming it's a typo or an unspecified unit of distance, we need more context to match it meaningfully to the formula.
3. An object travels 500 miles at a rate of 100 miles per hour.
- The time it takes can be calculated as:
[tex]\[
\text{Time} = \frac{\text{Distance}}{\text{Rate}} = \frac{500 \text{ miles}}{100 \text{ miles/hour}} = 5 \text{ hours}
\][/tex]
- If we plug this into the equation [tex]\(100 \times x = 500\)[/tex], where [tex]\(x\)[/tex] represents the time, we find [tex]\(x = 5\)[/tex].
- Thus, this situation matches the formula.
4. An object travels 100 inches per minute for 500 minutes.
- The total distance traveled here is:
[tex]\[
\text{Distance} = \text{Rate} \times \text{Time} = 100 \text{ inches/minute} \times 500 \text{ minutes} = 50000 \text{ inches}
\][/tex]
- This does not match [tex]\(500 = 100 \times x\)[/tex] as the total is 50000 inches.
Based on this analysis, the third situation ("An object travels 500 miles at a rate of 100 miles per hour") accurately fits the formula [tex]\(500 = 100x\)[/tex].
1. An object travels at 500 miles per hour for 100 hours.
- The formula suggests finding [tex]\(x\)[/tex] such that [tex]\(500 = 100 \times x\)[/tex].
- In this scenario, the distance the object would cover is:
[tex]\[
\text{Distance} = \text{Speed} \times \text{Time} = 500 \text{ miles/hour} \times 100 \text{ hours} = 50000 \text{ miles}
\][/tex]
- This does not match the formula [tex]\(500 = 100x\)[/tex].
2. An object travels 500 diret for 100 seconds.
- The term 'diret' is unclear, but assuming it's a typo or an unspecified unit of distance, we need more context to match it meaningfully to the formula.
3. An object travels 500 miles at a rate of 100 miles per hour.
- The time it takes can be calculated as:
[tex]\[
\text{Time} = \frac{\text{Distance}}{\text{Rate}} = \frac{500 \text{ miles}}{100 \text{ miles/hour}} = 5 \text{ hours}
\][/tex]
- If we plug this into the equation [tex]\(100 \times x = 500\)[/tex], where [tex]\(x\)[/tex] represents the time, we find [tex]\(x = 5\)[/tex].
- Thus, this situation matches the formula.
4. An object travels 100 inches per minute for 500 minutes.
- The total distance traveled here is:
[tex]\[
\text{Distance} = \text{Rate} \times \text{Time} = 100 \text{ inches/minute} \times 500 \text{ minutes} = 50000 \text{ inches}
\][/tex]
- This does not match [tex]\(500 = 100 \times x\)[/tex] as the total is 50000 inches.
Based on this analysis, the third situation ("An object travels 500 miles at a rate of 100 miles per hour") accurately fits the formula [tex]\(500 = 100x\)[/tex].
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