This paper identifies the relevance of a distributed source coding problem first formulated by Yeung and Zhang in 1999 to two applications in network design: i) the design of delay mitigating codes, and ii) the design of network coded P2P networks. When transmitting time-sensitive frames from a source to a destination over a multipath network using a collection of coded packets, the decoding requirements determine which subsets of packets will be sufficient for decoding which frames. The rate region of packet sizes consistent with these requirements is shown to be an instance of the aforementioned distributed source coding problem. When encoding file chunks into packets in a peer to peer system, the peers wish to receive their chunks as soon as possible while uploading data at as low a rate as possible. It is shown that the region of encoded packet sizes consistent with the decoding constraints is another instance of the aforementioned distributed source coding problem. These rate regions are placed in the larger context of rate-delay tradeoffs in designing delay mitigating codes and efficient P2P systems.