The table shows the number of miles driven over time. Express the relationship between distance and time in simplified form as a unit rate. Determine which statement correctly interprets this relationship. time (hours) 2 5 7 10 distance (miles) 135 337.5 472.5 675
To find the unit rate, we need to divide the distance by the time.
For the first interval of 2 hours, the distance is 135 miles.
So, the unit rate for the first interval is 135 miles / 2 hours = 67.5 miles/hour.
For the second interval of 3 hours (5 - 2), the distance is 337.5 miles (337.5 - 135).
So, the unit rate for the second interval is 337.5 miles / 3 hours = 112.5 miles/hour.
For the third interval of 2 hours (7 - 5), the distance is 472.5 miles (472.5 - 337.5).
So, the unit rate for the third interval is 472.5 miles / 2 hours = 236.25 miles/hour.
For the final interval of 3 hours (10 - 7), the distance is 675 miles (675 - 472.5).
So, the unit rate for the final interval is 675 miles / 3 hours = 225 miles/hour.
Overall, the relationship between distance and time is described by the following unit rates:
2 hours: 67.5 miles/hour
3 hours: 112.5 miles/hour
2 hours: 236.25 miles/hour
3 hours: 225 miles/hour
Therefore, the correct statement that interprets this relationship is:
As time increases by 1 hour, the distance driven increases by approximately 112.5 miles.