短语讲解：

1. As Americans discuss the issue of income inequality in an election year, a new study says rich people will live up to 15 years longer than poor ones.

live up to 不辜负; 履行; 达到高标准
例句：I had to live up to my oath.
我必须履行我的宣誓。

2. The difference in length of life as it relates to income is part of a new study published in the Journal of the American Medical Association.

relate to 涉及; 同…有…关系; 与…协调
例句：All these questions relate to philosophy.
这些问题都跟哲学有关。

3. At the same time, poor people will struggle even more in depressed cities.

at the same time 同时; 一起; 但是
例句：At the same time he still believed himself financially honest.
同时，他还认为自己在经济上是正直无欺的。