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

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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) About Me  (Show Source):
You can put this solution on YOUR website!
Let +d+ = the one-way distance to the mountains in miles
Let +s+ = his speed going to the mountains in mi/hr
+s+%2B+27+ = his speed on the trip home in mi/hr
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equation for going to the mountains:
(1) +d+=+s%2A7+
equation for going back home:
(2) +d+=+%28+s+%2B+27+%29%2A4+
---------------------------------
Plug (1) into (2)
(2) +7s+=+%28+s+%2B+27+%29%2A4+
(2) +7s+=+4s+%2B+108+
(2) +3s+=+108+
(2) +s+=+36+
and
+s+%2B+27+=+63+
----------------------
(1) +d+=+s%2A7+
(1) +d+=+36%2A7+
(1) +d+=+252+
Boris lives 252 mi from the mountains
---------------------
check answer:
(2) +d+=+%28+s+%2B+27+%29%2A4+
(2) +d+=+63%2A4+
(2) +d+=+252+
OK

Answer by josgarithmetic(39617) About Me  (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.

system%28%28r%29%287%29=d%2C%28r%2B27%29%284%29=d%29

Answer by MathTherapy(10552) About Me  (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: D%2F7+=+D%2F4+-+27

4D = 7D - 756 ----- Multiplying by LCD, 28

4D - 7D = - 756

- 3D = - 756

D, or distance = highlight_green%28matrix%281%2C4%2C+%28-+756%29%2F%28-+3%29%2C+or%2C+252%2C+miles%29%29

See how easy that was? Nothing complex!!