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Geometry Level 2

Agatha is at point \(A,\) and needs to reach her son Damien at point \(D\) as soon as possible. She can swim at a constant rate, and she can also run along the shore at a constant rate (her swimming and running speeds are different).

The diagram shows how long each segment takes her to travel. A direct route \(A \rightarrow D\) takes 61 s, but so does a route of \(A \rightarrow B \rightarrow C \rightarrow D.\)

Find the minimum possible amount of time (in seconds) required for Agatha to reach Damien.

Segments \(\overline{AB}\) and \(\overline{CD}\) are perpendicular to the shoreline.

Segments \(\overline{AB}\) and \(\overline{CD}\) are perpendicular to the shoreline.

Note: When Agatha swims to and from the shoreline, the angles don't have to be 90 degrees.

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