诚恳请教一道语法题

请教一个句子

1  the productivity of a job can be improved by seperating the components of a task into individual parts.

我很疑惑， 按照逻辑意思来解题，seperating的主语就是productivity, 怎么可能？

但是这是正确选项， 还有3天考试，请求NN帮我解答一下。

另外还有一句,也是有同样的问题

2     Peter annouced a plan to impose new control on pollution from trucks and buses engines by jointly adopting emmission limits that would be far stricker than the fedural rules.

请问这个 adopting的主语又是什么呢？？