Mr wang made up his mind to devote all the time he could spa

devote to (doing) sth.to...有两种词性：一是“不定式符号”,表明后面是一动词（原形）,即我们常见的：to do sth.二、更多的时候,to 是一个普通的“介词” （doing) sth (noun or pron)一说你就知道：e.g.Let's to to school.He'll come to the company...How can I get to the museum?这些句子中的to 都是你熟悉的介词,当它后跟名词或代词时,你没有觉得什么特别的.但如果遇到动词,就要将 do sth 改成 doing sth,因为道理很简单,动词不能做介词宾语.类似的常见短语中含介词 to (doing)sth：pay attention to doing.be used to doing...contribute to doing...be dedicated to doing = devoted,look forward to doing.,etc.
或者你可以记住这种固定用法.至于下面这道估计你困惑于时态.那么请看这句话后面的cared这个作为动词用了过去时,说明这是说的一个过去的状态,所以devote在这要用devoted

devote sth to doing 把某物奉献于做某事，to 是介词, 后跟动名词。不是不定式。
devoted作mr Wang的谓语，表过去时态。