SOLUTION: Two hikers start from the same point and hike in opposite directions around a lake whose shoreline is 19 mi long. One hiker walks 0.5 mph faster than the other hiker. How fast did

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Question 833264: Two hikers start from the same point and hike in opposite directions around a lake whose shoreline is 19 mi long. One hiker walks 0.5 mph faster than the other hiker. How fast did each hiker walk if they meet in 2 h?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of the distances they walk
has got to add up to 19 mi
Let +d+ = the distance the slower hiker travels in miles
+19+-+d+ = the distance the faster hiker travels in miles
Let +s+ = the slower hiker's speed in mi/hr
+s+%2B+.5+ = the faster hiker's speed in mi/hr
The time is +2+ hrs for both hikers
-----------------------------------
Equation for the slower hiker:
(1) +d+=+s%2A2+
Equation for faster hiker:
(2) +19+-+d+=+%28+s%2B.5+%29%2A2+
-------------------------
Substitute (1) into (2)
(2) +19+-+2s+=+%28+s%2B.5+%29%2A2+
(2) +19+-+2s+=+2s+%2B+1+
(2) +4s+=+18+
(2) +s+=+4.5+ mi/hr
and
+s+%2B+.5+=+5+ mi/hr
--------------------
The slower hiker's speed is 4.5 mi/hr
The faster hiker's speed is 5 mi/hr
-----------
check:
(2) +19+-+d+=+%28+s%2B.5+%29%2A2+
(2) +19+-+d+=+5%2A2+
(2) +d+=+9+ mi
and
(1) +d+=+s%2A2+
(1) +d+=+4.5%2A2+
(1) +d+=+9+ mi
OK