Alonzo drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 10 hours. When Alonzo drove home, there was no traffic and the trip only took 7 hours. If his average rate was 18 miles per hour faster on the trip home, how far away does Alonzo live from the mountains?
Do not do any rounding.

I know I'm setting it up wrong because I keep getting a negative answer. Here is my work,
Rate Time Distance
Trip 1 x 10 x
Trip 2 x+18 7 x

So, I did x=10x+7(x+18)

Question

Alonzo drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 10 hours. When Alonzo drove home, there was no traffic and the trip only took 7 hours. If his average rate was 18 miles per hour faster on the trip home, how far away does Alonzo live from the mountains? 
Do not do any rounding.

I know I'm setting it up wrong because I keep getting a negative answer. Here is my work, 
            Rate  Time  Distance
Trip 1    x        10         x
Trip 2  x+18     7         x

So, I did  x=10x+7(x+18)

anonymous · Answer

roofies lol

phi · Answer

you are close.  But you must use a different variable name for distance, because x cannot be both speed  and distance.

phi · Answer

Rate * Time  = Distance
Trip 1    x      *  10   =      y
Trip 2  (x+18) *  7    =     y

anonymous · Answer

So y=10x+7(x+18)

phi · Answer

the distance is the same for both trips, so we can set both to the same thing (y)

**
So y=10x+7(x+18)
***
no.

you have
Trip 1    x      *  10   =      y
Trip 2  (x+18) *  7    =     y

phi · Answer

you might notice that y equals y
and use that idea

anonymous · Answer

ohh, so two different equations.
10x=7x+126  
3x=126
x=42

phi · Answer

yes.