To find the time it took Stu to hike the trail one way, we can use the equation given:
3t = 5(3 - t)
Expanding the right side, we get:
3t = 15 - 5t
Adding 5t to both sides, we get:
8t = 15
Dividing both sides by 8, we get:
t = 15/8 = 1.875 hours
Therefore, it took Stu 1.875 hours to hike the trail one way.
To find the length of the trail, we can use the formula:
distance = rate x time
When hiking, Stu traveled at a rate of 3 miles per hour, so the distance he covered in one way is:
distance = 3 x 1.875 = 5.625 miles
Since Stu hiked the trail one way and then ran back on the same trail, the total length of the trail is twice the distance he covered in one way:
total distance = 2 x 5.625 = 11.25 miles
Therefore, the trail is 11.25 miles long.
To find the total distance Stu traveled, we can add the distance he covered while hiking to the distance he covered while running back:
total distance = 5.625 + 5.625 = 11.25 miles
Therefore, Stu traveled a total distance of 11.25 miles.