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This problem trains for: AMC-8, AMC-10, AIME, Math Kangaroo 7-8, Math Kangaroo 9-10.

The Cutty Sark, one of the fastest tall ships of all time, sailed at an average of 10 knots for 10 nautical miles. Then, the wind improved and her average speed increased by 10% for another 10 nautical miles. After this, there was a lull in the wind and her speed decreased by 10% for another 10 nautical miles. What was her average speed, in knots, for the 30 nautical miles?

The Cutty Sark has been restored and is open for visiting in Greenwich, UK.

The average speed of the ship must be computed using the definition:

equation

The total distance is:

equation

and the total time is the sum of the times spent sailing each leg:

equation

equation

equation

equation

The average speed, in knots, is:

equation