A tricky running problem I'm having trouble with the following problem:

Tom starts running towards a park which is at $800$m from him at speed
  $20$ m/s.  Kate who starts running with Tom at $25$ m/s goes back and
  forth between park and Tom until Tom reaches the park. 
Find total distance covered  by Kate.

I calculated the sum until Tom and Kate meet each other the second time, and I get the total distance covered by Kate until that time to be $800+88.9+88.9$.
However after that the calculations become too complex. Is there any other way to do this?

The key is that it doesn't matter "where" Kate runs ; we only want to know the distance she runs, and since we know her speed it suffices to know how long she's been running. Since she runs as long as Tom does, we only need to look at Tom's speed and distance. The solution with the geometric series is uselessly over-descriptive but correct too.
Hope that helps,
