Two runners, one averaging 9 miles per hour and the other averaging 6 miles per hour, start at the same place and run along the same trail. the slower runner arrivers at the end of the trail half hour after the faster runner. how far did each person run?

First, set up variables for each runner to calculate the time:
x = faster runner
x + 0.5 = slower runner

Next, set up an equation:
9x = 6(x + 0.5)
9x = 6x + 3
3x = 3
x = 1

Since both of the runners are starting at the same place and running on the same trail, they will run the same distance. They both ran 1 mile.