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Question

Consider the following for the next three (03) items that follow:
Two trains A and B started from stations P and Q respectively towards each other. Train A started at 7 p.m. at a speed of 60 km/hr and train B started at 4 a.m. (next day) at a speed of 90 km/hr. The distance between the two stations P and Q is 800 km.

How far from station Q will the two trains meet?
 

This question was previously asked in
CDS 2 2024 Maths Question Paper (01-Sep-2024)
The correct answer is
156 km

Train Meeting Distance Calculation

This problem requires us to determine the exact location where two trains, Train A and Train B, will cross paths. They are traveling towards each other from different stations, P and Q, and commence their journeys at different times. Our goal is to find the distance of this meeting point measured from station Q.

Problem Details

  • Total distance between stations P and Q: 800 km
  • Train A departs from station P at 7 p.m.
  • Speed of Train A: 60 km/hr
  • Train B departs from station Q at 4 a.m. on the following day.
  • Speed of Train B: 90 km/hr

Solving for Meeting Point from Station Q

  1. Determine the Head Start of Train A.

    First, we must account for the time Train A travels before Train B starts. Train A begins at 7 p.m., and Train B begins at 4 a.m. the next day. The duration between these two start times is 9 hours (from 7 p.m. to midnight is 5 hours, and from midnight to 4 a.m. is 4 hours).

    Time Train A travels alone = 9 hours

  2. Calculate Distance Covered by Train A During Head Start.

    Train A covers a certain distance during these 9 hours. We use the formula: Distance = Speed \(\times\) Time.

    Distance covered by Train A = Speed of Train A \(\times\) Time Train A travels alone

    Distance_A_initial = \(60 \text{ km/hr} \times 9 \text{ hr}\)

    Distance_A_initial = \(540 \text{ km}\)

  3. Find the Remaining Distance Between Trains.

    When Train B starts at 4 a.m., Train A has already traveled 540 km from station P. The distance remaining between the two trains is the total distance minus the distance Train A has covered.

    Remaining Distance = Total Distance PQ - Distance_A_initial

    Remaining Distance = \(800 \text{ km} - 540 \text{ km}\)

    Remaining Distance = \(260 \text{ km}\)

    At 4 a.m., the trains are 260 km apart and are moving towards each other.

  4. Calculate the Relative Speed of the Trains.

    Since both trains are moving towards each other, their speeds combine to close the distance between them. This combined speed is called the relative speed.

    Relative Speed = Speed of Train A + Speed of Train B

    Relative Speed = \(60 \text{ km/hr} + 90 \text{ km/hr}\)

    Relative Speed = \(150 \text{ km/hr}\)

  5. Determine Time Until the Trains Meet.

    Now we calculate how long it will take for the trains to cover the remaining 260 km distance at their relative speed. Using the formula: Time = Distance / Speed.

    Time to meet = Remaining Distance / Relative Speed

    Time to meet = \(260 \text{ km} / 150 \text{ km/hr}\)

    Time to meet = \(\frac{260}{150} \text{ hr} = \frac{26}{15} \text{ hr}\)

  6. Calculate the Meeting Point Distance from Station Q.

    The question asks for the distance from station Q. This is the distance Train B travels from station Q until they meet. Using the formula: Distance = Speed \(\times\) Time.

    Distance from Q = Speed of Train B \(\times\) Time to meet

    Distance from Q = \(90 \text{ km/hr} \times \frac{26}{15} \text{ hr}\)

    Distance from Q = \(\frac{90 \times 26}{15} \text{ km}\)

    Distance from Q = \(6 \times 26 \text{ km}\)

    Distance from Q = 156 km

Therefore, the two trains will meet 156 km away from station Q.

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Similar Questions

  1. Train \(X\) crosses a man standing on the platform in 24 seconds and train \(Y\) crosses a man standing on the platform in 18 seconds. They cross each other while running in opposite directions in 20 seconds. What is the ratio of speed of \(X\) to speed of \(Y\)?

  2. At what time will the two trains meet?

  3. If the lengths of the two trains A and B are 400 m and 500 m respectively, then what is the time taken by them to cross each other?
     


Important Questions from Problem on Trains

  1. Eight railway stations A, B, C, D, E, F, G and H are connected either by two-way passages or one-way passages. One-way passages are from C to A, E to G, B to F, D to H, G to C, E to C and H to G. Two-way passages are between A and E, G and B, F and D, and E and D.

    If the route between G and C is closed, which one of the following stations need not be passed through while travelling from H to C?

  2. A daily train is to be introduced between station A and station B starting from each end at 6 AM and the journey is to be completed in 42 hours. What is the number of trains needed in order to maintain the Shuttle Service?

  3. A train with a uniform speed passes a 122 meters long platform in 17 seconds and a 210 meters long bridge in 25 seconds. The speed of the train is:

  4. How long does a train 153 meters long running at the rate of 90 kmph take to cross a bridge 622 meters in length?

  5. A train passes a 360 metre long platform in 40 seconds and a man standing on the platform in 16 seconds. The speed of the train is:

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