Sampling Distributions · Superchallenge problem

A town is $60\%$ rural and $40\%$ urban. Rural incomes have mean $50$ and SD $10$; urban incomes have mean $60$ and SD $20$ (thousands of dollars). A simple random sample of $100$ residents is compared with a stratified sample of $60$ rural and $40$ urban residents, whose estimate is $0.6\bar x_{\text{rural}} + 0.4\bar x_{\text{urban}}$. Treating the town as very large, by what factor is the variance of the simple random sample's mean larger than the variance of the stratified estimate? Express your answer as a common fraction.