I there little more than a week when i set to work with the

I there little more than a week when i set to work with the scientist中间缺的部分应该是什么?
请帮忙讲解一下,开头空出的部分应当是什么呢?时态的问题

I had been there a little more than a week when I set to work with the scientist.
本句话的意思是：我在那儿呆了一个多星期之后,才开始和那位科学家一起着手工作.
本句中set应该是“过去时”,前面的谓语动词早于set to work因此要用“过去完成时”.