Question : The two stations are 120 km apart on a straight line. A train starts from station A at 8 a.m. and moves towards station B at 20 km/hr, and another train starts from station B at 9 a.m. and travels towards station A at a speed of 30 km/hr. At what time will they meet?
Option 1: 10:30 a.m.
Option 2: 10:00 a.m.
Option 3: 11:00 a.m.
Option 4: 11:30 a.m.
Correct Answer: 11:00 a.m.
Solution :
The first train travels for one hour before the second train starts, so it covers (20 × 1) = 20 km
The remaining distance between the two trains = (120 – 20) = 100 km
When both trains are moving, their combined speed = 20 + 30 = 50 km/hr
Therefore, the time it takes for the two trains to meet = $\frac{100}{50}$ hr = 2 hr
Since the second train starts at 9 a.m., the two trains will meet 2 hours after that, which is at 11 a.m.
Hence, the correct answer is at 11:00 a.m.
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