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Two towns are 1250 miles apart. A group of hikers start from each town and walks down the trail toward each other. They meet after hiking 200 hours. If one group travels 2 1/2 miles per hour slower than the other group, find the rate of each group.

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  1. Today, 22:30
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    Speed of faster group is 4.375 mph and slower group is 1.875 mph

    Step-by-step explanation:

    Let the travelling speed of the slow hikers be (x) mph.

    speed of the faster hikers will be (x + 2.50) mph

    The distance covered by both groups after 1 hour is x + (x + 2.50) miles = 2x + 2.50 miles.

    Since distance=Speed*time then

    when the two groups meet after 200 hours, they have covered the whole distance when combined hence

    1250 = (2x + 2.50) * 200

    400x + 500 = 1250

    400x = 1250 - 500 = 750

    x = 750/400 = 1.875 mph.

    x + 2.50 = 1.875+2.50 = 4.375 mph

    Therefore, speed of faster group is 4.375 mph and slower group is 1.875 mph
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