Alice and Bob live on the same road. At time t, they both decide to walk to each other’s houses at constant speed. However, they were busy thinking about math so that they didn’t realize passing each other. Alice arrived at Bob’s house at 3:19 \mathrm{pm}, and Bob arrived at Alice’s house at 3: 29 \mathrm{pm}. Charlie, who was driving by, noted that Alice and Bob passed each other at 3: 11 \mathrm{pm}. Find the difference in minutes between the time Alice and Bob left their own houses and noon on that day.