Two hikers set out on a trail that is 4 miles long. One is walking at a rate of 3.3 mph and the other is jogging at a rate of 5.5 mph. Once a hiker reaches the end of the trail, he immediately turns around and starts jogging back at the same rate. What distance away from the start of the trail will the two hikers meet each other?

We first find the time it takes for the jogger to reach the end.

distance = (rate) (time) so it follows that time = distance / rate

time = 4 / (5.5) = 0.7272 hours

Then we find the distance the walker travels.

distance = (3.3) (0.7272) = 2.4 miles

Then we create two equations. Let d represent the distance from the start of the trail and t represent the time in hours since the jogger turns back. The jogger has the equation

d = 4 miles + (-5.5 mph) (t)

and the walker has the equation

d = 2.4 miles + (+3.3 mph) (t)

If we solve this system of equations, we get a solution of t = 0.182 and d = 3.

The answer to this question is that the two hikers will meet each other 3 miles away from the start of the trail.