Question
Download Solution PDFA train leaves Hyderabad at 4:00 A.M. and reaches Vijayawada at 8:00 A.M. the same day. Another train leaves Vijayawada at 6:00 A.M. and reaches Hyderabad at 9:30 A.M the same day. At what time do the two trains cross each other?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
A train leaves Hyderabad at 4:00 A.M. and reaches Vijayawada at 8:00 A.M. the same day. Another train leaves Vijayawada at 6:00 A.M. and reaches Hyderabad at 9:30 A.M the same day.
Formula used:
Let the two trains meet at t hours after 6:00 A.M.
Speed of Train 1 = Distance / Time = D / 4 hours
Speed of Train 2 = Distance / Time = D / 3.5 hours
Relative speed when moving towards each other = (D/4) + (D/3.5)
Calculation:
Distance covered by Train 1 in t hours = (D/4) × (t + 2)
Distance covered by Train 2 in t hours = (D/3.5) × t
Since the total distance covered by both trains is D:
⇒ (D/4) × (t + 2) + (D/3.5) × t = D
⇒ (t + 2)/4 + t/3.5 = 1
⇒ (t + 2)/4 + t/3.5 = 1
⇒ (7(t + 2) + 4t) / 28 = 1
⇒ 7t + 14 + 4t = 28
⇒ 11t + 14 = 28
⇒ 11t = 14
⇒ t = 14 / 11
⇒ t = 1.27 hours
⇒ t ≈ 1 hour 16 minutes
So, the two trains cross each other approximately 1 hour and 16 minutes after 6:00 A.M.
∴ The correct answer is option (4) 6:56 A.M.
Last updated on Jul 1, 2025
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