Jack and Jill may be skating still

Jack and Jill are skating. Jill has a mass of \(50~\mbox{kg}\), Jack has a mass of \(80~\mbox{kg}\). At \(t = 0~\mbox{seconds}\) Jill starts skating across a \(50~\mbox{m}\) diameter rink at a speed of \(3~\mbox{m/s}\). After \(3~\mbox{seconds}\) Jack skates after her with a speed of \(5~\mbox{m/s}\). When they meet, Jack scoops up Jill and they glide to the other end of the rink together. At what time \(t\) in seconds do they reach the other side of the rink? You can neglect any friction of the ice or drag.

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