Returning home,she began to cook.
现在分词短语表示时间,相当于一个时间状语从句：
Hearing the news,they all jumped with joy.
Returning home,he began to do his homework.
Having finished her work,she went home.为什么要用现在分词短语she后面用began 不是应该一直的吗现在分词短语作状语，其逻辑主语应该和句子的主语是一致的。Returning home, she began to cook.(主语都是指she)现在分词作时间状语，相当于 when 等引起的从句。 When she returned home, she began to cook.