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?

$$800\frac{25}{20}=1000$$
Kate ran for the same lapse of time as Tom.
