SOLUTION: Floyd can walk 2mph faster than his wife, Rachel. It takes Rachel 3 hr longer than Floyd to hike a 12-mile trail through the park. Find their speeds.

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Question 1056739: Floyd can walk 2mph faster than his wife, Rachel. It takes Rachel 3 hr longer than Floyd to hike a 12-mile trail through the park. Find their speeds.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = Rachel's speed in mi/hr
+s+%2B+2+ = Floyd's speed in mi/hr
Let +t+ = Floyd's time in hrs
+t+%2B+3+ = Rachel's time in mi/hr
---------------------------------------
Floyd's equation:
(1) +12+=+%28+s+%2B+2+%29%2At+
Rachel's equation:
(2) +12+=+s%2A%28+t+%2B+3+%29+
----------------------------
(1) +t+=+12%2F%28+s+%2B+2+%29+
Substitute (1) into (2)
(2) +12+=+s%2At+%2B+3s+
(2) +12+=+s%2A%28+12%2F%28+s+%2B+2+%29+%29+%2B+3s+
Multiply both sides by +s+%2B+2+
(2) +12%2A%28+s+%2B+2+%29+=+12s+%2B+3s%2A%28+s+%2B+2+%29+
(2) +12s+%2B+24+=+12s+%2B+3s%5E2+%2B+6s+
(2) +3s%5E2+%2B+6s+-+24+=+0+
(2) +s%5E2+%2B+2s+-+8+=+0+
(2) +%28+s+%2B+4+%29%2A%28+s+-+2+%29+=+0+
+s+=+2+ ( I can't use +s+=+-4+, since it's negative )
and
+s+%2B+2+=+4+
------------------
Rachel's speed is 2 mi/hr
Floyd's speed is 4 mi/hr
---------------------------
check:
(1) +12+=+%28+s+%2B+2+%29%2At+
(1) +12+=+4t+
(1) +t+=+3+
and
(2) +12+=+s%2A%28+t+%2B+3+%29+
(2) +12+=+2%2A%28+t+%2B+3+%29+
(2) +6+=+t+%2B+3+
(2) +t+=+3+
OK