Sampling Distributions · Superchallenge problem

Two independent polls estimate the same proportion $p = 0.5$: one samples $400$ voters, the other $900$. Analyst A reports the simple average $\dfrac{\hat p_1 + \hat p_2}{2}$; analyst B pools all $1300$ responses into one proportion. By what factor is the variance of A's estimate larger than the variance of B's? Express your answer as a common fraction.