Travel Time of Trains Meeting Each Other

CAT 2022 Slot 1 · QA · Medium · Speed Time Distance

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Trains A and B start traveling at the same time towards each other with constant speeds from stations X and Y, respectively. Train A reaches station Y in 10 minutes while train B takes 9 minutes to reach station X after meeting train A. Then the total time taken, in minutes, by train B to travel from station Y to station X is

  1. A.

    15

  2. B.

    12

  3. C.

    6

  4. D.

    10

Answer

A

Explanation

Let tt be the time (in minutes) taken by both trains from start until they meet. Train A's total travel time is 10 minutes. So time taken by Train A after meeting to reach Y is 10−t10 - t. Train B's time taken after meeting to reach X is b=9b = 9 minutes.

Using the standard formula for meeting trains: t=ta×tbt = \sqrt{t_a \times t_b} where ta=10−tt_a = 10 - t and tb=9t_b = 9. t=(10−t)×9t = \sqrt{(10 - t) \times 9} t2=9(10−t)t^2 = 9(10 - t) t2+9t−90=0t^2 + 9t - 90 = 0 (t+15)(t−6)=0(t + 15)(t - 6) = 0

Since time cannot be negative, t=6t = 6 minutes.

Train B's total time taken to travel from Y to X is: Total time=t+tb=6+9=15 minutes.\text{Total time} = t + t_b = 6 + 9 = 15\text{ minutes.}

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