When will the fast runner overtake the slower runner on a circular 200-m track?

[donald1403]

Two runners start simultaneously from the same point on a circular 200-m track and run in the same direction. One runs at constand speed of 6.20 m/s and the other at a constant speed of 5.50 m/s. When will the fast one overtake("lap") the slower one and how far from the starting point will each have run?

please help thx.

st

 

[berkeman]

Show us how you think you should set up the algebra to solve this. Think of it in terms of some number of 200m laps plus a little extra. The faster runner runs one more lap than the slower runner, plus that same extra fraction of a lap (which could be zero if the numbers were set up that way).

 

[kyle8921]

The fast runner will overtake the slower runner when he has completed one full lap around the track. This will occur at a time of 32.26 seconds since the track is 200 meters and the fast runner is running at a constant speed of 6.20 m/s. At this time, the slower runner will have run 176.5 meters (5.50 m/s x 32.26 s = 176.5 m) and the fast runner will have run 200 meters. Therefore, the fast runner will overtake the slower runner at a distance of 23.5 meters from the starting point.