SOLUTION: Boris drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 7 hours. When Boris drove home, there was no traffic and the trip only took 4

Question 1056985: Boris drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 7 hours. When Boris drove home, there was no traffic and the trip only took 4 hours. If his average rate was 27 miles per hour faster on the trip home, how far away does Boris live from the mountains?
Found 3 solutions by josmiceli, josgarithmetic, MathTherapy:
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
Let = the one-way distance to the mountains in miles
Let = his speed going to the mountains in mi/hr
= his speed on the trip home in mi/hr
-------------------------------------------------------
equation for going to the mountains:
(1)
equation for going back home:
(2)
---------------------------------
Plug (1) into (2)
(2)
(2)
(2)
(2)
and

----------------------
(1)
(1)
(1)
Boris lives 252 mi from the mountains
---------------------
check answer:
(2)
(2)
(2)
OK
Answer by josgarithmetic(39618)   (Show Source): You can put this solution on YOUR website!

SPEED TIME DISTANCE GOINGTO r 7 d RETURNING r+27 4 d

Basic Constant Travel Rate Rule, RT=D.

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

Boris drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 7 hours. When Boris drove home, there was no traffic and the trip only took 4 hours. If his average rate was 27 miles per hour faster on the trip home, how far away does Boris live from the mountains?

With D being the distance, the SPEED equation you need is:
4D = 7D - 756 ----- Multiplying by LCD, 28
4D - 7D = - 756
- 3D = - 756
D, or distance =
See how easy that was? Nothing complex!!
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