Two towns are 1250 miles apart A group of hikers starts from

Two towns are 1250 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 200 hours. If one group travels 21/2 mile per hour slower than the other group, find the rate of each group The rate of the slower group is (Simplify your answer)

Solution

Let the travelling rate/speed of the slower hikers’ group be x mph. Then the travelling rate/speed of the faster hikers’ group is x + 2.50 mph. The distance covered by both these hikers’ group, together, in an hour is x + ( x + 2.50) miles = 2x + 2.50 miles.We know that d = rt, where d is the distance, r is the rate of travel/speed, and t is time. Since the two groups of hikers meet after 200 hours, we have 1250 = (2x + 2.50)*200 or, 400x + 500 = 1250 or, 400x = 1250 -500 = 750 so that x = 750/400 = 1.875 mph. Then x + 2.50 = 1.875+2.50 = 4.375 mph. Thus, the travelling rate/speed of the slower hikers’ group is 1.875 mph and that of the faster hikers’ group is 4.375 mph.