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.

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

25/6 hope it : )

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