Sarah Speed and Hi Velocity are racing cars around a track. If Sarah can make a complete circuit in 72 seconds and Hi completes a circuit in 68 seconds. How many seconds will it take for Hi to catch up to Sarah?

Question

Sarah Speed and Hi Velocity are racing cars around a track.  If Sarah can make a complete circuit in 72 seconds and Hi completes a circuit in 68 seconds.  How many seconds will it take for Hi to catch up to Sarah?

anonymous · Answer

Catch up to her as in like... take a lap on her?

anonymous · Answer

I guess so. The answer my professor got was 1224 seconds, but idk how she got that.

anonymous · Answer

Since the cars are going around periodically, I think the best way to keep track of their position is with a sinusoidal curve.  Then try to find out the the time at which their position is the same.

anonymous · Answer

You could ignore the fact that the track is circular and project their position onto the $x$ axis.  The only catch is that you have to make sure that they aren't on different sides of the track when they are in the same position.

anonymous · Answer

I don't understand what you're talking about :(