With the old man ----- the way,we had no difficulty in findi

the old man 是动词LEAD的主语,WITH SOMEBODY DOING SOMETHING .独立主格可以以 with 引导,也可以不用 with,但其主语都要用主格,而相当于谓语的部分（对主语的动作或状态进行描述的部分）却绝对不能用谓语形式.
这叫with复合结构,有：with sb/sth +prep.
with sb/sth +p.p.
with sb/sth +doing
with sb/sth +adj.
with sb/sth +adv.
with sb/sth +to do