In this paper, the average successful throughput, i.e., goodput, of a coded 3-node cooperative network is studied in a Rayleigh fading environment. It is assumed that a simple automatic repeat request (ARQ) technique is employed in the network so that erroneously received packets are retransmitted until successful delivery. The relay is assumed to operate in either amplify-and-forward (AF) or decode-and-forward (DF) mode. Under these assumptions, retransmission mechanisms and protocols are described, and the average time required to send information successfully is determined. Subsequently, the goodput for both AF and DF relaying is formulated. The tradeoffs and interactions between the goodput, transmission rates, and relay location are investigated and optimal strategies are identified.