Cassie leaves Escanaba at 8:30 AM heading for Marquette on her bike. She bikes at a uniform rate of 12 miles per hour. Brian leaves Marquette at 9:00 AM heading for Escanaba on his bike. He bikes at a uniform rate of 18 miles per hour. They both bike on the same 50-mile route between Escanaba and Marquette. At what time in the morning do they meet? (Express your answer in standard hh:mm time form.)
Let the time that it takes you to meet each other==T
12T + 18[T - 1/2]==50
12T + 18T - 9 == 50
30T ==50 + 9
T ==59/30 x 60 minutes ==118 minutes after Cassie left at 8:30 AM
8:30 + 118 minutes ==10:28 AM - the exact time when you will meet.
Note: Cassie will have ridden her bike for 118 minutes and you will have ridden your bike for 118 - 30 ==88 minutes after you left at 9:00 AM.