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AnilSinghBora
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A train covered a certain distance at a uniform speed. If the train would have been 10 km/h faster, it would have taken 2 hours less than the scheduled time. And, if the train were slower by 10 km/h; it would have taken 3 hours more than the scheduled time. Find the distance covered by the train. Q.3

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How i solve this optional chapter question, of exercise 3.7 in easiest way . I think it is also an important type of question. A train covered a certain distance at a uniform speed. If the train would have been 10 km/h faster, it would have taken 2 hours less than the scheduled time. And, if the train were slower by 10 km/h; it would have taken 3 hours more than the scheduled time. Find the distance covered by the train.

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  1. Let the speed of the train be A km/hr and the time taken by the train to travel a distance be N hours and the distance to travel be X hours.

    Speed of the train = Distance travelled by train / Time taken to travel that distance

    A = N (distance)/ X (time)

    Or, N = AX – – – – – – – – – – – (1)

    Using the information that is given, we get:

    (A+10) = X/(N-2)

    (A + 10) (N – 2) = X

    AN + 10N – 2A – 20 = X

    By using the equation (1) we get,

    – 2A + 10N = 20 – – – – – – – – – – (2)

    (A-10) = X/(N+3)

    (A – 10) (N + 3) = X

    AN – 10N + 3A – 30 = X

    By using the equation (1) we get,

    3A – 10N = 30 – – – – – – – – – (3)

    Adding equation (2) and equation (3) we get,

    A = 50

    Using the equation (2) we get,

    (-2) x (50) + 10N = 20

    -100 +10N = 20

    => 10N = 120

    N = 12hours

    From the equation (1) we get,

    Distance travelled by the train, X = AN

    = 50 x 12

    = 600 km

    Hence, the distance covered by the train is 600km.

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