Answer :
Sure! Let's go through each option to see which situation matches the formula [tex]\(500 = 100x\)[/tex].
### Situation 1:
An object travels 500 miles at a rate of 100 miles per hour.
The formula to use here is:
[tex]\[ \text{Distance} = \text{Rate} \times \text{Time} \][/tex]
We have:
- Distance = 500 miles
- Rate = 100 miles per hour
Applying these to the formula:
[tex]\[ 500 = 100 \times x \][/tex]
This means the time [tex]\(x\)[/tex] would be 5 hours, as it fits perfectly into [tex]\(500 = 100 \times 5\)[/tex].
This situation matches the formula.
### Situation 2:
An object travels 500 feet for 100 seconds.
Using the same formula:
[tex]\[ \text{Distance} = \text{Rate} \times \text{Time} \][/tex]
We have:
- Distance = 500 feet
- Time = 100 seconds
The equation becomes:
[tex]\[ 500 = \text{Rate} \times 100 \][/tex]
Solving for the rate:
[tex]\[ \text{Rate} = 5 \text{ feet per second} \][/tex]
The equation does not fit the form [tex]\(500 = 100x\)[/tex] directly.
This situation does not match the formula.
### Situation 3:
An object travels at 500 miles per hour for 100 hours.
Using the formula:
[tex]\[ \text{Distance} = \text{Rate} \times \text{Time} \][/tex]
We have:
- Rate = 500 miles per hour
- Time = 100 hours
This gives:
[tex]\[ \text{Distance} = 500 \times 100 = 50,000 \text{ miles} \][/tex]
This is not the same as [tex]\(500 = 100x\)[/tex] because the numbers are different.
This situation does not match the formula.
### Situation 4:
An object travels 100 inches per minute for 500 minutes.
Using the formula:
[tex]\[ \text{Distance} = \text{Rate} \times \text{Time} \][/tex]
We have:
- Rate = 100 inches per minute
- Time = 500 minutes
The equation becomes:
[tex]\[ \text{Distance} = 100 \times 500 = 50,000 \text{ inches} \][/tex]
Again, this is not the same as [tex]\(500 = 100x\)[/tex].
This situation does not match the formula.
In conclusion, the situation that matches the formula [tex]\(500 = 100x\)[/tex] is:
An object travels 500 miles at a rate of 100 miles per hour.
### Situation 1:
An object travels 500 miles at a rate of 100 miles per hour.
The formula to use here is:
[tex]\[ \text{Distance} = \text{Rate} \times \text{Time} \][/tex]
We have:
- Distance = 500 miles
- Rate = 100 miles per hour
Applying these to the formula:
[tex]\[ 500 = 100 \times x \][/tex]
This means the time [tex]\(x\)[/tex] would be 5 hours, as it fits perfectly into [tex]\(500 = 100 \times 5\)[/tex].
This situation matches the formula.
### Situation 2:
An object travels 500 feet for 100 seconds.
Using the same formula:
[tex]\[ \text{Distance} = \text{Rate} \times \text{Time} \][/tex]
We have:
- Distance = 500 feet
- Time = 100 seconds
The equation becomes:
[tex]\[ 500 = \text{Rate} \times 100 \][/tex]
Solving for the rate:
[tex]\[ \text{Rate} = 5 \text{ feet per second} \][/tex]
The equation does not fit the form [tex]\(500 = 100x\)[/tex] directly.
This situation does not match the formula.
### Situation 3:
An object travels at 500 miles per hour for 100 hours.
Using the formula:
[tex]\[ \text{Distance} = \text{Rate} \times \text{Time} \][/tex]
We have:
- Rate = 500 miles per hour
- Time = 100 hours
This gives:
[tex]\[ \text{Distance} = 500 \times 100 = 50,000 \text{ miles} \][/tex]
This is not the same as [tex]\(500 = 100x\)[/tex] because the numbers are different.
This situation does not match the formula.
### Situation 4:
An object travels 100 inches per minute for 500 minutes.
Using the formula:
[tex]\[ \text{Distance} = \text{Rate} \times \text{Time} \][/tex]
We have:
- Rate = 100 inches per minute
- Time = 500 minutes
The equation becomes:
[tex]\[ \text{Distance} = 100 \times 500 = 50,000 \text{ inches} \][/tex]
Again, this is not the same as [tex]\(500 = 100x\)[/tex].
This situation does not match the formula.
In conclusion, the situation that matches the formula [tex]\(500 = 100x\)[/tex] is:
An object travels 500 miles at a rate of 100 miles per hour.
