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 $$74$$ kilometers after biking for $$2$$ hours, jogging for $$3$$ hours, and swimming for $$4$$ hours, while Sue covers $$91$$ kilometers after jogging for $$2$$ hours, swimming for $$3$$ hours, and biking for $$4$$ 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.

(第二十六届AIME1 2008 第3题)