It's a sunny Sunday afternoon, about 17 degrees and you are walking around a lake enjoying the early signs of spring. The sidewalk is crowded with runners and walkers. You notice a runner approaching you wearing a t-shirt with writing on it. You read the first two lines, but are unable to read the third and final line before he passes. You wonder, "Hmmm, if he continues around the lake, I bet I'll see him again, but should I anticipate the time when we'll pass again." You look at your watch and it is 3:07 p.m. You recall the lake is M miles in circumference. You estimate your walking speed at 3 miles per hour and the runner's speed to be about 7 miles per hour. What is the time you need to wait until you see the runner again?
I'll give two methods for solving this. One is more physical and uses the relative velocity: Since you are actually approaching the runner along the circumference of a circle his/her relative velocity ...
This job focuses on calculating the time for runners' crossing.