你以上三个句子中reason后接的why从句和that从句都是定语从句。reason后的why从句全部是定语从句，没有同位语动词。why通常不需要翻译，但受汉语说话习惯，你翻译为为什么...的原因也可以。reason后接的that从句可能是定语从句，也可能是同位语从句。如果是定语从句，that可以用why替换，翻译的方法相同。如果that引导同位语从句，通常翻译为...这个原因或...这样的原因。例如：你母亲生病了，这是你上学迟到的原因。The reason why you were late  to school was that your mother was ill.

The teacher asked you the reason why/that you were late. 这里why/that引导定语从句。

You told the teacher that your mother was ill.  

The teacher accepted the reason that your mother was ill. 这个that从句就是同位语从句。老师接受了你母亲生病了这个原因。而不是你母亲为什么生病。这个that从句不可以用why引导。

仔细体会这个例子中定语从句和同位语从句的区别。

如果that引导的是同位语从句，则reason和that从句就可以写成下面的句子：

The reason was that my mother was ill.

如果that引导的是定语从句，就不可以写成这样的句子：

The reason was that I was late.