Jinghua hiked 4.5 miles through the woods in 2.25 hours. She hiked the return trip at the same average rate but by a different route, taking 2.5 hours. How many miles did Jinghua hike on the return trip?
Jinghua hiked 5 miles on the return trip.
To find the distance Jinghua hiked on the return trip, we first determine her average speed during the initial hike. She hiked 4.5 miles in 2.25 hours, giving her an average speed of 2 miles per hour. Maintaining this speed, we can calculate the distance for the return trip, which took her 2.5 hours.
This choice suggests that Jinghua hiked 4.75 miles on the return trip. However, using her average speed of 2 miles per hour over 2.5 hours results in a distance of 5 miles (2 miles/hour × 2.5 hours = 5 miles). Thus, 4.75 miles is incorrect.
This is the correct answer. Jinghua's average speed was 2 miles per hour, and over 2.5 hours, she would cover a distance of 5 miles (2 miles/hour × 2.5 hours = 5 miles). This aligns perfectly with the calculation based on her speed and time.
Choosing 5.5 miles indicates a miscalculation of distance based on her speed and time. At 2 miles per hour, she could only travel 5 miles in 2.5 hours. Therefore, 5.5 miles exceeds the calculated distance.
This option implies that Jinghua hiked 6 miles on the return trip, which would mean she would have to hike at a speed greater than her initial average. Given her average speed of 2 miles per hour, 6 miles would require 3 hours, making this answer impossible for a 2.5-hour return hike.
Jinghua's return trip distance can be accurately determined by her consistent average speed. She maintained a speed of 2 miles per hour, resulting in a 5-mile hike over 2.5 hours. The other options fail to align with this calculation, reinforcing the understanding that her return distance was indeed 5 miles.
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