A train leaves station M at 7 a.m. and reaches station N at 11 a.m. Another train leaves N at 8 a.m. and reaches M at 2 p.m. Both run at uniform speeds on parallel tracks. At what time will they meet?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 9:48 a.m.
The distance is not given, so take a convenient value: the LCM of the two journey times, 4 h and 6 h, that is 12 units. The first train runs alone for one hour; after that the gap closes at the sum of the two speeds.
Speed of the train from M \(\displaystyle =\frac{12}{4}=3\) units per hour; speed of the train from N \(\displaystyle =\frac{12}{6}=2\) units per hour
By 8 a.m. the train from M has covered 3 units, so the gap is \(12-3=9\) units
Time to close the gap \(\displaystyle =\frac{9}{3+2}=\frac{9}{5}\) hours \(=1\) hour 48 minutes
Meeting time \(=8\) a.m. \(+\) 1 hour 48 minutes \(=9{:}48\) a.m.