# Three amigos

Margo and Sven are outside in a field, standing right next to each other and talking. We'll put x,y coordinates on the field and measure everything in meters. Ursula, a friend of both Margo and Sven, is also outside walking due north (positive y-direction) at $$1~\mbox{m/s}$$. When Ursula crosses the origin (at $$t=0$$) Margo and Sven (at coordinates $$(100,0)$$) notice her and decide to walk over and say hello.

Margo knows a little physics, and so she figures out how she should walk at $$2~\mbox{m/s}$$ to meet Ursula in the shortest amount of time. Sven doesn't know any physics, so he just always walks directly towards Ursula, also at $$2~\mbox{m/s}$$, until he catches up to her.

If the time Sven meets Ursula is $$t_s$$ and the time Margo meets Ursula is $$t_m$$, what is $$t_s-t_m$$ in seconds?

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