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Two towns are 1300 miles apart. A group of hikers starts from each town and walks down the trail toward each other. They meet after a total hiking time of 240 hours. If one group travels 2 1/2 miles per hour slower than the other group, find the rate of each group.

Two towns are 1300 miles apart A group of hikers starts from each town and walks down the trail toward each other They meet after a total hiking time of 240 hou class=

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240(v+2.5)=1300-240v

240v+600=1300-240v

480v=1900

v=95/24

v-2.5=v-5/2

95/24-60/24=35/24

So the faster group travels at 95/24 mph (≈3.96 mph) and the slower group travels at 35/24 mph (≈1.46mph)

check...

240(95/24)=950 miles from the origin...

1300-240(35/24)=950 miles from the origin...

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