▲句子语法结构分析如下

(1)状语：In the 100-yard relay

(2)主语：our team

(3)谓语：impressed

(4)宾语：the crowd

(5)状语：with each of the members shaving off her own best time

▲以上考察with非谓语动词的独立结构作句子状语

With+名词+现在分词 结构

with each of the members shaving several seconds off her own best time

备注：each of the members 为现在分词逻辑主语，非谓语动词自带逻辑主语，不是句子主语，称为非谓语动词独立主格结构）

▲附：英语独立主格结构的用法

独立主格结构主要表示谓语动词发生的时间、原因、条件或伴随情况等，相当于一个状语从句或并列句。     

(1) 用作时间状语(名词+过去分词）

The work done (=After the work had been done), we went home. 工作完成后，我们就回家了。

(2) 用作条件状语（名词+现在分词）

Weather permitting (=If weather permits), they will go on an outing to the beach tomorrow. 如果天气允许的话，他们将在明天组织一次海滨小游。

(3) 用作原因状语（名词+不定式）

An important lecture to be given tomorrow (=As an important lecture will be given tomorrow), the professor has to stay up late into the night. 因为明天要发表一个重要的演讲，教授不得不熬夜到很晚。

(4) 用作伴随状语（名词+过去分词；改为并列句）

He was lying on the grass, his hands crossed under his head (=and his hands were crossed under his head). 他躺在草地上，两手交叉枕在脑后。

(5) 表示补充说明（名词+形容词）

A hunter came in, his face red with cold (=and his face was red with cold). 一个猎人走了进来，他的脸冻得通红。

We redoubled our efforts, each man working like two. 我们加倍努力，一个人干两个人的活。

备注：独立主格结构表示时间、条件或原因时，相当于一个状语从句，一般放在句首，表示原因时还可放在句末；表伴随状况或补充说明时，相当于一个并列句，通常放于句末。