# 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?

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I did the sum until Tom and Kate meet each other the second time so I get total distance covered by Kate until that to be 800+88.9+88.9. However after that the calculations become too complex is there any other way to do this – Sudhanshu Aug 4 '14 at 15:57
Easier: How long does Tom run? How long does Kate run? – hardmath Aug 4 '14 at 15:59
Tom runs for 40 s so does that mean Kate covers 25 *40 = 1000 m Is it that simple!! Please tell me if I am doing it right – Sudhanshu Aug 4 '14 at 16:01
This is a very similar problem to the famous fly puzzle. See here primepuzzle.com/leeslightest/howfar.html – Mathmo123 Aug 4 '14 at 16:38
1000 meters in 40 seconds has got to be a new world record. – kasperd Aug 4 '14 at 21:56

$$800\frac{25}{20}=1000$$ Kate ran for the same lapse of time as Tom.
In other words, you don't need to know the time. After any amount of time, Kate has run $25$% ($25/20=1.25 => 25$%) further than Tom. – Scott Aug 4 '14 at 20:11