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