The rate of the slower hiker is 1.1 mph and the rate of the faster hiker is 6.6 mph
Step-by-step explanation
One hiker walks 5.5 mph faster than the other.
Suppose, the speed of the slower hiker is (x) mph.
So, the speed of the faster hiker will be:
(x+5.5)mph
Both hikers are walking toward each other and meet in 10 hours.
We know that, Distance = speed * time
So, the distance walked by the slower hiker in 10 hours = 10x miles and the distance walked by the faster hiker in 10 hours = 10(x + 5.5) miles.
Given that, they were 77 miles apart in the beginning. So the equation will be ...
10x + 10(x + 5.5) = 77
10x + 10x + 55 = 77
20x = 77 - 55 = 22
x = 22/20 = 1.1
Thus, the rate of the slower hiker is 1.1 mph and the rate of the faster hiker is (1.1 + 5.5) mph = 6.6 mph