Chimpanzee mothers

"Modern human begins come from a few million years ago where the life expectancy was around 30, more or less. Then, biology did not expect for the human female to reach menopause. Nevertheless, the life expectancy began to rise near the 20th century. But that is a digression.

Since it was a life of 30 years, half of that was set aside for child rearing.

Do the math. Once a female had a kid or two, she didn't NEED to win another mate."

No.
Common ancestor of man and chimpanzee was closer to chimpanzee than to man.
From
http://www.sciencemag.org/news/2007/12/menopause-chimps
Of 185 female chimpanzees followed in the wild, just 34 lived to the age of 40 - but nearly half of those who survived past 40 gave birth past 40, and one gave birth at age 55.

So: Why is it so easy to tell apart a 15 year old woman and a 35 year old woman by look? Both are fertile.