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For one mile, Percy travels at an average speed of one mile an hour. For the...

For one mile, Percy travels at an average speed of one mile an hour. For the subsequent mile he travels at an average speed of two miles an hour. He continues this upward trend, for each subsequent mile he increases his average speed from the previous mile by one mile per hour. Let k be the smallest integer such that after traveling for k miles, Percy’s average speed from the beginning of the trip is greater than 2 miles an hour. What is k? Express Percy's average speed for this value of k as a fraction in lowest terms.
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