Chessboard race

This week’s Fiddler is a puzzle with a surprise connection to physics!

A tiny ant is racing across a 2-by-2 chessboard, as shown below, where each smaller square has a side length of 1 cm. The ant starts at the bottom-left corner of the bottom-left black square and is trying to reach the top-right corner of the top-right black square. The ant moves faster on the white squares than on the black squares. Speed on the white squares is 1 cm per minute, while speed on the black squares is 0.9 cm per minute. What’s the least amount of time it will take the ant to reach the finish?

Extra Credit: Instead, the board is now 8-by-8, as shown below.

My solution:
[Show Solution]

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