The separation between two stations A and B is 450 km. A train begins at 4 pm…

2023

The separation between two stations A and B is 450 km. A train begins at 4 pm from A and moves towards B at a normal velocity of 60 km/hr. Another train begins from B at 3.20 p.m and moves towards A at a normal velocity of 80 km/hr. How a long way from A will the two train s meet and what time?

  1. A.

    6.50 PM

  2. B.

    5.50 PM

  3. C.

    5.59 PM

  4. D.

    5.89 PM

Attempted by 1 students.

Show answer & explanation

Correct answer: A

Step-by-Step Solution

To solve this, we must synchronize the start times of both trains.

  1. Account for the head start:

    • The train from station B starts at 3:20 PM, and the train from station A starts at 4:00 PM.

    • The train from B has a head start of 40 minutes (4:00 PM - 3:20 PM).

    • Distance covered by B in 40 minutes:

      • Speed of B = 80 km/hr.

      • Time = 40 minutes = 40/60 hours = 2/3 hours.

      • Distance = Speed × Time = 80 × (2/3) = 160/3 km (approx. 53.33 km).

  2. Calculate the remaining distance at 4:00 PM:

    • Total separation = 450 km.

    • Distance remaining to be covered by both trains starting from 4:00 PM = 450 - (160/3) = (1350 - 160) / 3 = 1190/3 km.

  3. Determine Relative Speed:

    • Since the trains are moving towards each other, their relative speed is the sum of their individual speeds.

    • Relative Speed = 60 km/hr + 80 km/hr = 140 km/hr.

  4. Calculate time taken to meet after 4:00 PM:

    • Time = Remaining Distance / Relative Speed

    • Time = (1190/3) / 140 = 1190 / (3 × 140) = 1190 / 420 = 119 / 42 hours = 17 / 6 hours.

    • 17/6 hours = 2 hours and 50 minutes.

  5. Determine the meeting time:

    • Meeting Time = 4:00 PM + 2 hours 50 minutes = 6:50 PM.

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