原句：He was the first person that passed the examination。
转换：He was the first person passing the examination
原句：This is the best way that can solve the problem
转换：This is the best way solving the problem
原句：who is the girl that is talking with tom？
转换：who is the girl talking with tom？
我做的这些转换都对吗，如有不对之处，请详细指正！
to solve the problem应该是best way的定语吧？
追答是的。
动词不定式作后置定语。