Two hikers start from the same point and hike in opposite directions around a lake whose shoreline is 11 mi long. one hiker walks 0.5 mph faster than the other hiker. how fast did each hiker walk if they meet in 2 h?

This is a problem that can be solved using algebraic substitution. If we define A and B to be the speeds of the two walkers in mph then we know that one of them is 0.5 mph faster than the other. The order here doesn't matter but we'll define B as A + 0.5. Additionally we know that distance = speed times time therefore the two speeds of the hikers combined multiplied by the time (t) must give 11 miles as that is the circumference of the lake: At + Bt = 11 (2) As we know the relation between A and B is: B = A + 0.5 we can say At + (A + 0.5)t = 11 2At + 0.5t = 11 we know that t is 2 hours so: 2*2A + 0.5*2 = 11 4A + 1= 11 A = 2.5 as B = A + 0.5 then B = 3