159k views
5 votes
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.

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 traveled?


miles

User Asleep
by
8.0k points

1 Answer

5 votes
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.
User Camenwolf
by
7.9k points