Ned is flying an airplane that is currently right over his house. His altitude is 5000 m, and his velocity is 600 km/h, due north. At the same moment, Carmine is 10 km due west of Ned's house. Carmine's altitude is 1000 m, and his velocity is 420 km/h due east. Carmine is climbing at 100m/min. At what time t will the planes be closest together, and what will be that distance?