SOLUTION: Two country sides are 1100 miles apart. A group of hikers starts from each country side and walks down the trail toward each other. They meet after a total hiking time of 220 hours

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Question 1054160: Two country sides are 1100 miles apart. A group of hikers starts from each country side and walks down the trail toward each other. They meet after a total hiking time of 220 hours. If one group travels 2 and 1/2 miles per hour slower than the other group, find the rate of each group.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
A trick I use is to let one of the groups
remain stationary and let the other group
travel at the sum of their speeds
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Let +r+ = the rate of the faster group in mi/hr
+r+-+2.5+ = the rate of the slower group in mi/hr
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+1100+=+%28+r+%2B+r+-+2.5+%29%2A220+
+1100+=+%28+2r+-+2.5+%29%2A220+
+1100+=+440r+-+550+
+440r+=+1650+
+r+=+3.75+
and
+r+-+2.5+=+3.75+-+2.5+
+r+-+2.5+=+1.25+
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The slower group's rate is 1.25 mi/hr
The faster group's rate is 3.75 mi/hr
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check:
+d%5B1%5D+=+1.25%2A220+
+d%5B1%5D+=+275+
and
+d%5B2%5D+=+3.75%2A220+
+d%5B2%5D+=+825+
-----------------------
+d%5B1%5D+%2B+d%5B2%5D+=+275+%2B+825+
+d%5B1%5D+%2B+d%5B2%5D+=+1100+
OK