Two points P and Q are 240 km apart. Train A starts from P towards Q at 60 km/h at 9:00 AM. Train B starts from Q towards P at 80 km/h at 10:00 AM. At what time will they meet?
Explanation:
By 10:00 AM, Train A covers 60 km. Remaining distance = 240 - 60 = 180 km. Relative speed = 60 + 80 = 140 km/h. Time to meet after 10 AM = 180 / 140 = 9/7 hours = 1 hour and 17 minutes. Meeting time is 11:17 AM.
A carriage driving in a fog passed a man who was walking at the rate of 3 km/h in the same direction. He could see the carriage for 4 minutes and it was visible to him up to a distance of 100 meters. What is the speed of the carriage?
Explanation:
Time = 4 minutes = 4/60 = 1/15 hour. Distance = 100 meters = 0.1 km. Relative speed = Distance / Time = 0.1 / (1/15) = 1.5 km/h. Since the carriage moves in the same direction, Relative Speed = Speed of carriage - Speed of man => 1.5 = Speed of carriage - 3 => Speed of carriage = 4.5 km/h.
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