A uniform horizontal walkway AB AB\,AB has length 4 m and mass 10 kg. It is held by vertical cables at A A\,A and BBB. The cable at A A\,A can support at most 700 N and the cable at B B\,B can support at most 400 N. A person of mass 60 kg walks from A A\,A towards BBB. The person is modelled as a particle at distance x x\,x m from AAA.
Determine the greatest possible value of x x\,x for which neither cable is overloaded. Use g=9.8g=9.8g=9.8 m s−2^{-2}−2.