A train leaves City A heading east at 60 mph. Thirty minutes later, another train departs City B heading west toward City A at 80 mph. They meet between the cities. Without knowing the distance between the cities, can you say where they meet relative to City A or B?
Hints
Use ratios of speeds and the remaining gap at the moment the second train starts.
Answer
By the time the second train departs, the first train has traveled 30 miles. The closing speed is 140 mph (60 + 80), so the distances covered after the second train leaves stay in a 60:80 = 3:4 ratio. The meeting point therefore sits 3/7 of the remaining distance from City A and 4/7 from City B, allowing you to describe it purely by ratio without ever needing the absolute distance.