Find the rate of each group

Question

Two towns are 1050 miles apart. A group of hikers start from each town and walk the trail toward each other. They meet after a total hiking time of 200 hours. If one group travels 1/2 mile per hour faster than the other​ group, find the rate of each group.

Answer 1

Let r = rate of the slower group and r + (1/2) is the rate of the faster group.

Each group walks 200 hours and the total distance traveled is 1050 miles.

One group travels 200r and the other group travels 200(r+.5)

200r + 200r + 100 = 1050

400r=950

You can do the necessary arithmetic.