SOLUTION: A camper drove 80 mi to a recreational area and then hiked 4 mi into the woods. The rate of the camper while driving was ten times the rate while hiking. The time spent hiking and

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A camper drove 80 mi to a recreational area and then hiked 4 mi into the woods. The rate of the camper while driving was ten times the rate while hiking. The time spent hiking and       Log On


   

Question 1198710: A camper drove 80 mi to a recreational area and then hiked 4 mi into the woods. The rate of the camper while driving was ten times the rate while hiking. The time spent hiking and driving was 3 h. Find the rate at which the camper hiked.
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52756) About Me  (Show Source):
You can put this solution on YOUR website!
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A camper drove 80 mi to a recreational area and then hiked 4 mi into the woods.
The rate of the camper while driving was ten times the rate while hiking.
The time spent hiking and driving was 3 h. Find the rate at which the camper hiked.
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Let x be the rate of hiking; 10x be the rate of driving.


The time equation is

    80%2F%2810x%29 + 4%2Fx = 3  hours.


Simplify and find x

    8%2Fx + 4%2Fx = 3

    12%2Fx = 3

    x = 12%2F3 = 4.


ANSWER.  The rate of hiking is 4 miles per hour.  The rate of driving is 40 miles per hour.

Solved.



Answer by greenestamps(13196) About Me  (Show Source):
You can put this solution on YOUR website!


The ratio of the two distances is 80:4 = 20:1, and the ratio of the rates is 10:1. That means the ratio of the two times is 20:10 = 2:1.

The total times was 3 hours; so the camper spent 2 hours driving and 1 hour hiking.

The camper hiked 4 miles in 1 hours, so his speed was 4 miles per hour.

ANSWER: 4mph