# Thread: People Moving Around Circle Track

1. ## People Moving Around Circle Track

Bob and Sally are each going for a run around a circlar track of radius 80 feet. They start running from different locations on the circle.
Bob starts at the easternmost point and jogs 10 feet/second around the track in the clockwise direction.
Sally runs counterclockwise at 14 feet/second and passes Bob for the first time in 16 seconds.
(Words I bolded are the given information we need)

Find Sally's x and y coordinates in 12 minutes.
So here is what I'm thinking on a coordinate plan
Bob starts at the easternmost point (meaning all the way on the right), at (80,0)
Sally is somewhere
Circumference: 2πr = 2π(80) = 160π feet, π is pi by the way. This is the full length track.
Though, I'm still confused on how to start out.
Can someone help?
Thanks

2. ## Re: People Moving Around Circle Track

Hi,

Here's a blueprint to solve this problem:

1) You may write the positions on the track as a function of an angle which varies with time because Bob and Sally are moving. Let's call this angle $\theta$.
2) Find $\theta$ as a function of time for each runner
3) Using the previous functions, you can use the time at which they first meet in order to find where does Sally start running

I hope this helps