Final answer:
The car, traveling at a constant average speed calculated from given intervals, will travel approximately 31.714 miles in 37 minutes and about 51.429 miles in 1 hour.
Step-by-step explanation:
The student is asking how far a car will travel in 37 minutes and in 1 hour, given that it travels 2 miles in 2 1/3 minutes and 3 miles in 3 1/2 minutes. To solve this, we first calculate the car's average speed using these two scenarios and then apply it to find the distance it would travel in the specified times.
First, we find the average speed for each given time interval:
For 2 miles in 2 1/3 minutes, the average speed is 2 miles / (7/3 minutes) = 6/7 miles per minute.
For 3 miles in 3 1/2 minutes, the average speed is 3 miles / (7/2 minutes) = 6/7 miles per minute.
Noticing that both scenarios yield the same average speed, we can use this speed to calculate the distance traveled in 37 minutes and 1 hour:
Distance in 37 minutes = (6/7 miles/minute) * 37 minutes = 31.714 miles (rounded to three decimal places).
Distance in 1 hour (60 minutes) = (6/7 miles/minute) * 60 minutes = 51.429 miles (rounded to three decimal places).
Hence, the car will travel approximately 31.714 miles in 37 minutes and approximately 51.429 miles in 1 hour.