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Ed and Sue

Source: AIME 2008I Problem 3

March 23, 2008
modular arithmeticcalculusintegrationAMC

Problem Statement

Ed and Sue bike at equal and constant rates. Similarly, they jog at equal and constant rates, and they swim at equal and constant rates. Ed covers 74 74 kilometers after biking for 2 2 hours, jogging for 3 3 hours, and swimming for 4 4 hours, while Sue covers 91 91 kilometers after jogging for 2 2 hours, swimming for 3 3 hours, and biking for 4 4 hours. Their biking, jogging, and swimming rates are all whole numbers of kilometers per hour. Find the sum of the squares of Ed's biking, jogging, and swimming rates.