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Tired Birds…May Miss Each Other on a Cloudy Day

There are three birds in a tree. One flies toward the east going 1 mile the first day, 2 the second, 3 the third and so on. The second flies toward the west going 1 miles the first day, 8 the second, 27 the third and so on according to the cubes of the numbers. The distance around the earth is believed to be 44,310 miles. In how many days did the two birds meet?

Solution:

Source: J. Cardano’s Practica Arithmetice, 1539