SOLUTION: Amy drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 8 hours. When Amy drove home, there was no traffic and the trip only took 5 hou

Algebra.Com
Question 891313: Amy drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 8 hours. When Amy drove home, there was no traffic and the trip only took 5 hours. If her average rate was 21 miles per hour faster on the trip home, how far away does Amy live from the mountains?
Do not do any rounding.
Found 2 solutions by Alan3354, Edwin McCravy:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Amy drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took hours. When Amy drove home, there was no traffic and the trip only took hours. If her average rate was miles per hour faster on the trip home, how far away does Amy live from the mountains?
Do not do any rounding.
--------------
She lives miles from the mountains.
============
You're looking for free help, but you can't take the time to check what you post?
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
I put in some numbers.

Amy drove to the mountains last weekend. There was heavy traffic on the way
there, and the trip took 8 hours. When Amy drove home, there was no traffic and
the trip only took 5 hours. If her average rate was 21 miles per hour faster on
the trip home, how far away does Amy live from the mountains? 
Make this chart:

             | Distance |  rate | time
--------------------------------------
To mountains |          |       |  
To home      |          |       |

how far away does Amy live from the mountains?
Suppose Amy lives x miles from the mountains.

Fill in x as both distances and the times
going and coming 8 hours and 5 hours.  

             | Distance |  rate | time
To mountains |    x     |       |  8
Coming home  |    x     |       |  5



to fill in the two rate boxes:

             | Distance |  rate | time
To mountains |    x     |  x/8  |  8
Coming home  |    x     |  x/5  |  5

The equation comes from this sentence:
>>...her average rate was 21 miles per hour faster on the trip home...<<

       

  

Multiply through by LCD=40.

  

Subtract 5x from both sides:

  

Divide both sides by 3

  

So Amy lives 280 miles from the mountains.

Edwin
RELATED QUESTIONS

Rafael drove to the mountains last weekend. There was heavy traffic on the way there, and (answered by richwmiller)
Keisha drove to the mountains last weekend. There was heavy traffic on the way there, and (answered by mananth,MathTherapy)
Martina drove to the mountains last weekend. There was heavy traffic on the way there,... (answered by mananth)
Chau drove to the mountains last weekend. There was heavy traffic on the way there, and... (answered by ankor@dixie-net.com)
Elsa drove to the mountains last weekend. There was heavy traffic on the way there, and... (answered by lwsshak3,josmiceli)
Frank drove to the mountains last weekend. There was heavy traffic on the way there, and... (answered by ankor@dixie-net.com)
Ryan drove to the mountains last weekend. There was heavy traffic on the way there, and... (answered by ankor@dixie-net.com)
Bob drove to the mountains last weekend. There was heavy traffic on the way there, and... (answered by lwsshak3)
Alan drove to the mountains last weekend. There was heavy traffic on the way there, and... (answered by josmiceli)