You want to get across a square ploughed field from one corner
to the opposite corner as quickly as possible. There is a path
along one edge of the field but the rest of the field is ploughed
right up to the other three edges. On the ploughed land you can
walk at 6 km per hour. From where you are standing you can walk on
the path along one edge of the field at 10 km per hour (the path is
red in the interactivity below), but there are no paths along the
other edges of the field. What is the best route to take?

Suppose the edge of the field is one kilometre in length. What
is the shortest time in which you can cross the field to the
opposite corner?

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