Peter, Quincy, Rita, and Sam work in a toy assembly plant. On Wednesday Peter and Quincy started assembling at $7:00$ AM and were able to assemble $2$ toys per minute and $3$ toys per minute, respectively. At some later time, Rita and Sam joined the group, and Rita was able to assemble $4$ toys per minute, and Sam was able to assemble $1$ toy per minute. Together, they finished assembling $1200$ toys at exactly $9:30$ AM. At what time did Rita and Sam join the group?