Answer :
Sure! Let's solve the given question by looking at each provided situation and comparing them to the equation: [tex]\(500 = 100 \times x\)[/tex].
We can rewrite this equation as [tex]\(x = \frac{500}{100}\)[/tex], which simplifies to [tex]\(x = 5\)[/tex].
Now, let's determine which situations match this formula:
1. Situation 1: An object travels 100 inches per minute for 500 minutes.
- Here, the time is 500 minutes, and the rate is 100 inches per minute.
- The distance traveled would be: [tex]\(100 \times 500 = 50000\)[/tex] inches.
- Since [tex]\(50000\)[/tex] inches does not match our original equation where we need [tex]\(100 \times x = 500\)[/tex], this situation does not match.
2. Situation 2: An object travels 500 miles at a rate of 100 miles per hour.
- Here, the distance is 500 miles, and the rate is 100 miles per hour.
- To find the time taken, we can use the formula: [tex]\(\text{Time} = \frac{\text{Distance}}{\text{Rate}} = \frac{500}{100} = 5\)[/tex] hours.
- Since [tex]\(x = 5\)[/tex], this situation matches the equation [tex]\(100 \times x = 500\)[/tex].
3. Situation 3: An object travels at 500 miles per hour for 100 hours.
- Here, the rate is 500 miles per hour, and the time is 100 hours.
- The distance traveled would be: [tex]\(500 \times 100 = 50000\)[/tex] miles.
- Since [tex]\(50000\)[/tex] miles does not match our equation where it should be [tex]\(100 \times x = 500\)[/tex], this situation does not match.
4. Situation 4: An object travels 500 feet for 100 seconds.
- Here, the distance is 500 feet, and the time is 100 seconds.
- To find the rate, we can use the formula: [tex]\(\text{Rate} = \frac{\text{Distance}}{\text{Time}} = \frac{500}{100} = 5\)[/tex] feet per second.
- Since [tex]\(x = 5\)[/tex], this situation matches the equation [tex]\(100 \times x = 500\)[/tex].
So, the situations that match the equation are:
- Situation 2: An object travels 500 miles at a rate of 100 miles per hour.
- Situation 4: An object travels 500 feet for 100 seconds.
We can rewrite this equation as [tex]\(x = \frac{500}{100}\)[/tex], which simplifies to [tex]\(x = 5\)[/tex].
Now, let's determine which situations match this formula:
1. Situation 1: An object travels 100 inches per minute for 500 minutes.
- Here, the time is 500 minutes, and the rate is 100 inches per minute.
- The distance traveled would be: [tex]\(100 \times 500 = 50000\)[/tex] inches.
- Since [tex]\(50000\)[/tex] inches does not match our original equation where we need [tex]\(100 \times x = 500\)[/tex], this situation does not match.
2. Situation 2: An object travels 500 miles at a rate of 100 miles per hour.
- Here, the distance is 500 miles, and the rate is 100 miles per hour.
- To find the time taken, we can use the formula: [tex]\(\text{Time} = \frac{\text{Distance}}{\text{Rate}} = \frac{500}{100} = 5\)[/tex] hours.
- Since [tex]\(x = 5\)[/tex], this situation matches the equation [tex]\(100 \times x = 500\)[/tex].
3. Situation 3: An object travels at 500 miles per hour for 100 hours.
- Here, the rate is 500 miles per hour, and the time is 100 hours.
- The distance traveled would be: [tex]\(500 \times 100 = 50000\)[/tex] miles.
- Since [tex]\(50000\)[/tex] miles does not match our equation where it should be [tex]\(100 \times x = 500\)[/tex], this situation does not match.
4. Situation 4: An object travels 500 feet for 100 seconds.
- Here, the distance is 500 feet, and the time is 100 seconds.
- To find the rate, we can use the formula: [tex]\(\text{Rate} = \frac{\text{Distance}}{\text{Time}} = \frac{500}{100} = 5\)[/tex] feet per second.
- Since [tex]\(x = 5\)[/tex], this situation matches the equation [tex]\(100 \times x = 500\)[/tex].
So, the situations that match the equation are:
- Situation 2: An object travels 500 miles at a rate of 100 miles per hour.
- Situation 4: An object travels 500 feet for 100 seconds.
