SOLUTION: Joe Fleet jogs at 8 mph. Ron hikes at 4 mph. They start from opposite ends of a 44 mile hiking trail at the same. Time. How far does each go if Ron has 15 minutes to set up ca

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Question 190239: Joe Fleet jogs at 8 mph. Ron hikes at 4 mph. They start from opposite ends of a 44 mile hiking trail at the same. Time. How far does each go if Ron has 15 minutes to set up camp before Joe arrives?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
For Joe:
(1) d%5Bj%5D+=+r%5Bj%5D%2At%5Bj%5D
For Ron:
(2) d%5Br%5D+=+r%5Br%5D%2At%5Br%5D
given:
r%5Bj%5D+=+8 mi/hr
r%5Br%5D+=+4 mi/hr
d%5Bj%5D+%2B+d%5Br%5D+=+44 mi
t%5Bj%5D+=+t%5Br%5D+%2B+1%2F4 hr
----------------------
(1) d%5Bj%5D+=+8t%5Bj%5D
(2) d%5Br%5D+=+4t%5Br%5D
and
d%5Bj%5D+%2B+d%5Br%5D+=+44
d%5Bj%5D+=+44+-+d%5Br%5D
therefore
(1) 44+-+d%5Br%5D+=+8t%5Bj%5D
(2) d%5Br%5D+=+4t%5Br%5D
also
t%5Bj%5D+=+t%5Br%5D+%2B+1%2F4
therefore
(1) 44+-+d%5Br%5D+=+8%2A%28t%5Br%5D+%2B+1%2F4%29
(2) d%5Br%5D+=+4t%5Br%5D
-------------------------
(1) 44+-+d%5Br%5D+=+8t%5Br%5D+%2B+2
(1) 8t%5Br%5D+%2B+d%5Br%5D+=+42
and
(2) 4t%5Br%5D+-+d%5Br%5D+=+0
Add (1) and (2)
12t%5Br%5D+=+42
t%5Br%5D+=+3.5
and, since
(2) d%5Br%5D+=+4t%5Br%5D
d%5Br%5D+=+4%2A3.5
d%5Br%5D+=+14 mi
and also
d%5Bj%5D+%2B+d%5Br%5D+=+44
d%5Bj%5D+%2B+14+=+44
d%5Bj%5D+=+30 mi
Ron went 14 mi and Joe went 30 mi
check answer:
t%5Bj%5D+=+t%5Br%5D+%2B+1%2F4
t%5Bj%5D+=+3.5+%2B+.25
t%5Bj%5D+=+3.75
(1) d%5Bj%5D+=+8t%5Bj%5D
(1) 30+=+8%2A3.75
(1) 30+=+30
OK
and
(2) d%5Br%5D+=+4t%5Br%5D
(2) 14+=+4%2A3.5
(2) 14+=+14
OK