At what time 是介词短语,属于副词短语,整体可以视作“疑问副词（而不是疑问代词）”,在句中作时间状语,相当于 when 的作用.前者指“具体的时刻”,后者既可以指“时刻”,也可以指“日期”、“年代”等
本句的意思是问“你是在那个钟点到了火车站的?”,也可以改为 When did you arrive at the station?但是后者再没有语言情境的情况下,可能会误解为“那一天到了火车站”.
由于原句是疑问句,用的是倒装语序,因此在变成间接引语时需要调整语序.另外,它还是过去时,如果变成跟在 asked 或 told 等动词后的间接引语,“到达”的行为就成了过去的过去,需要用过去完成时表示,即——
He asked that at what time you had arrived at the station.
在非正式英语中还可以把介词 at 后置,变成 He asked that what time you had arrived at the station (at).
事实上,at what time 的介词 at 完全可以省略.如果说 at what time 是一种文绉绉的书面语（阳春白雪）的话,那么 what time 则是地道的口语（下里巴人）,而且He asked that what time you had arrived at the station更为常见.