Stu hiked a trail at an average rate of 3 miles per hour. He ran back on the same trail at an average rate of 5 miles per hour. He traveled for a total of 3 hours.

Question

The equation 3t = 5(3 – t) can be used to find the time it took Stu to hike one way.

How long did it take Stu to hike the trail one way?
_____ hours

How long is the trail?
_____ miles

What is the total distance Stu travelled?
_____ miles

Answer 1

To solve for the time it took Stu to hike the trail one way, we can plug in the values into the equation 3t = 5(3 - t) and solve for t:

3t = 5(3 - t)
3t = 15 - 5t
3t + 5t = 15
8t = 15
t = 15/8
t = 1.875 hours

So, it took Stu 1.875 hours to hike the trail one way.

To find the distance of the trail, we can multiply the time by the average rate:
Distance = 3 miles/hour x 1.875 hours = 5.625 miles

Therefore, the trail is 5.625 miles long.

The total distance Stu travelled is twice the distance of the trail, since he hiked one way and ran back. So the total distance is:
Total distance = 2 x 5.625 miles = 11.25 miles

Therefore, Stu travelled a total of 11.25 miles.