SOLUTION: 3. a hiker walks 6 miles into a forest on a trail that is mainly up hill. she walks down at a rate of 1.2 times as fast as she walked up. if the return trip takes 40 minutes (2/3 h

Question 228501: 3. a hiker walks 6 miles into a forest on a trail that is mainly up hill. she walks down at a rate of 1.2 times as fast as she walked up. if the return trip takes 40 minutes (2/3 hour) less than the hike up, at what rate did the hiker walk up the hill?

Answer by drj(1380) (Show Source): You can put this solution on YOUR website!
3. A hiker walks 6 miles into a forest on a trail that is mainly up hill. She walks down at a rate of 1.2 times as fast as she walked up. If the return trip takes 40 minutes (2/3 hour) less than the hike up, at what rate did the hiker walk up the hill?

Step 1. distance = speed * time

Step 2. Let x be the speed or rate of the hiker going up the hill.

Step 3. Let 1.2x be the speed or ate of the hiker going down the hill since she walks down at a rate 1.2 time as fast as she walked up.

Step 4. Then since the distance is 6 miles and the time for the return trip is 2/3 hour.

Step 5. Solve for in the equation using the following steps

Multiply by 3 to get rid of denominator

Divide by 2.4 to both sides of the equation

. Then check distance if 6 miles traveling at 9 miles per hour downhill. 9*2/3=6 miles which is a true statement.

Step 6. ANSWER: The hiker traveled at a speed of 7.5 miles per hour going up the hill.

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J

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