We study a lossy source-broadcasting problem involving the transmission of a binary source over a two-receiver erasure broadcast channel. The motivation of our work stems from the problem faced by a server that wishes to singly broadcast content to a diverse set of users with fractional source reconstruction requirements. In this problem, the server wishes to minimize the overall network latency incurred (measured by the number of channel uses per source symbol) when faced with users of heterogeneous channel qualities, computing capabilities, content demand etc. We provide two complementary approaches to this problem. The first approach is to consider the problem from a joint source-channel coding formulation. Under this formulation, we provide both inner and outer bounds for the network latency under an erasure distortion criterion. Alternatively, the second approach employs rateless coding and formulates an optimization problem so as to find a degree distribution that minimizes the network latency. We compare both approaches with numerical simulations.