Not only are the poor getting poorer but they're also living shorter lives than the rich.

A new study by the Brookings Institute shows a surprising trend -- the gap in life expectancy is widening based on income level.

That the rich outlive the poor isn't surprising since they've historically enjoyed better access to medicine, resources, education and food.

But the gap has been getting worse -- much worse.

On average, a rich man born in the U.S. in 1920 could expect to live about six years longer than a poor man born in the same year.

By 1940, this gap had more than doubled. Among rich and poor men born in 1940, the difference in life expectancy was 12 years.

This same trend was also seen with women's life expectancies.

The gap between rich and poor women widened from 3.7 years for women born in 1920 to 10.1 years for those born in 1940.

The researchers examined variables such as smoking, obesity, education, nutrition and exercise, but were unable to find a definitive cause for the growing disparity.

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Gary Burtless, one of the study's researchers, said the findings have big implications for Social Security.

As people live longer, concerns that Social Security benefits will run out have prompted some officials to consider trimming benefits. However, Burtless says blindly cutting benefits would disproportionately hurt the poor.

Lower-income workers tend to claim their pensions at a younger age than higher-income workers. Because working longer and waiting to claim benefits entitles workers to higher payouts, tapping into Social Security earlier is a disadvantage. Since they work less time over all, these lower-income workers receive lower monthly payments.

Add to this a shorter life span and lower-income workers end up getting less of the Social Security pot. That's why Burtless says making cuts across the board would end up hurting those who need these benefits the most.