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

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) (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 = the distance the slower hiker travels in miles
= the distance the faster hiker travels in miles
Let = the slower hiker's speed in mi/hr
= the faster hiker's speed in mi/hr
The time is hrs for both hikers
-----------------------------------
Equation for the slower hiker:
(1)
Equation for faster hiker:
(2)
-------------------------
Substitute (1) into (2)
(2)
(2)
(2)
(2) mi/hr
and
mi/hr
--------------------
The slower hiker's speed is 4.5 mi/hr
The faster hiker's speed is 5 mi/hr
-----------
check:
(2)
(2)
(2) mi
and
(1)
(1)
(1) mi
OK

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