Let \(\mathrm{t}\) be the number of hours, from 11:00 am, when Jimmy catches up with John. The time that Jimmy will have to drive to catch up with John is \(\mathrm{t}-1 / 4\) : he starts a quarter of an hour late. Whe Jimmy catches up with John, they would have traveled the same distance. Hence \(50 t=65(t-1 / 4)\)

Solve for \(t\)

\(50 t=65 t-65 / 4\)

\(t=65 / 60=1.083\) hours \(=1\) hour and 5 minutes

Jim will catch up with John at

11:00 am \(+1\) hour, 5 minutes \(=12: 05 \mathrm{pm}\)