2019 CIME I Problems/Problem 7

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Albert, Bob, Carrie, and Douglas are travelling along a road at constant (but not necessarily equal) velocities$.$ Albert meets Bob at $12:00 \text{pm},$ Carrie at $12:20 \text{pm}$ and Douglas at $12:32\text{pm}.$ Later that same day, Douglas meets Carrie at $12:53\text{pm}$ and Bob at $1:17\text{pm}.$ If Bob and Carrie meet $m$ minutes after noon, compute $m$.