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 m/s1~\mbox{m/s}. When Ursula crosses the origin (at t=0t=0) Margo and Sven (at coordinates (100,0)(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 m/s2~\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 m/s2~\mbox{m/s}, until he catches up to her.

If the time Sven meets Ursula is tst_s and the time Margo meets Ursula is tmt_m, what is tstmt_s-t_m in seconds?

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