SOLUTION: The Santa Fe National Historic Trail is approximately 1200 miles between Old Franklin, Missouri, and Santa Fe, New Mexico. Suppose that a group of hikers start from each town and w

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Question 336281: The Santa Fe National Historic Trail is approximately 1200 miles between Old Franklin, Missouri, and Santa Fe, New Mexico. Suppose that a group of hikers start from each town and walk the trail toward each other. They meet after a total hiking time of 240 hours. If one group travels at 1/2 mile per hour slower than the other group, find the rate of each group.
Answer by ankor@dixie-net.com(22740) (Show Source):
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Trail is approximately 1200 miles between Old Franklin, Missouri, and Santa Fe, New Mexico.
Suppose that a group of hikers start from each town and walk the trail toward each other.
They meet after a total hiking time of 240 hours.
If one group travels at 1/2 mile per hour slower than the other group,
find the rate of each group.
:
When they meet the distance of each group totals 1200 mi
:
Let s = speed of one group
then
(s+.5) = speed of the other group
:
Write a distance equation, dist = speed * time
240s + 240(s+.5) = 1200
240s + 240s + 120 = 1200
480s = 1200 - 120
480s = 1080
s =
s = 2.25 mph is one group
and
2.25 + .5 = 2.75 mph is the other group
:
:
See if that is true; find the distance traveled by each group
240(2.25) = 540 mi
240(2.75) = 660 mi
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total dist: 1200 mi