SOLUTION: Two cyclists start at the same point and travel in opposite directions. One travels 4 mph faster than the other. In 4 hours, they are 112 miles apart. Find how fast each is traveli

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Question 256713: Two cyclists start at the same point and travel in opposite directions. One travels 4 mph faster than the other. In 4 hours, they are 112 miles apart. Find how fast each is traveling.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
For the faster bicyclist:
d%5B1%5D+=+r%5B1%5D%2At%5B1%5D
For the slower bicyclist:
d%5B2%5D+=+r%5B2%5D%2At%5B2%5D
-----------------
given:
(1) r%5B1%5D+=+r%5B2%5D+%2B+4 mi/hr
(2) t%5B1%5D+=+4 hrs
(3) t%5B2%5D+=+4 hrs
(4) d%5B1%5D+%2B+d%5B2%5D+=+112
------------------
From (1), r%5B2%5D+=+r%5B1%5D+-+4
From (4), d%5B2%5D+=+112+-+d%5B1%5D
-----------------------
d%5B1%5D+=+r%5B1%5D%2A4
112+-+d%5B1%5D+=+%28r%5B1%5D+-+4%29%2A4
Substituting:
112+-+r%5B1%5D%2A4+=+r%5B1%5D%2A4+-+16
2%2Ar%5B1%5D%2A4+=+112+%2B+16
r%5B1%5D+=+128%2F8
r%5B1%5D+=+16
and, since
r%5B2%5D+=+r%5B1%5D+-+4
r%5B2%5D+=+16+-+4
r%5B2%5D+=+12
The faster bicyclist goes 16 mi/hr
The slower one goes 12 mi/hr