A railway engine travels with a speed of 90km/h. The decrease in its speed is directly proportional to the square root of the number of Wago

Question

A railway engine travels with a speed of 90km/h. The decrease in its speed is directly proportional to the square root of the number of Wagons attached to it. If 25 wagons attached, it can run at a speed of 60 km/h. What is the number of wagons attached to the engine if it runs at a speed of 54 km/h? *​

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Clara 3 weeks 2021-10-05T05:28:29+00:00 1 Answer 0 views 0

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    2021-10-05T05:29:33+00:00

    Solution :

    Given that, decrease in speed of train is directly proportional to the square root of the number of Wagons attached to it.

    So,

    Decrease in speed ∝ √(No. of wagons.)

    → Dec. in speed = k * √n [ k is constant term here and n = No. of wagons.)

    Now, given that,

    → speed of Train engine = 90km/h . (Mean with 0 wagons .)

    → when 25 wagons attached , speed becomes = 60km/h.

    So, we can say that,

    → Because of 25 wagons speed is decreased by = 90 – 60 = 30 km/h.

    A/q,

    Dec. in speed = k * √n

    → 30 = k * √25

    → 30 = k * 5

    → k = 6.

    Therefore, when speed is 54 km/h , speed is decreased by = 90 – 54 = 36 km/h.

    So,

    → Dec. in speed = k * √n

    → 36 = 6 * √n

    → 6 = √n

    → n = 36 wagons (Ans.)

    Hence, when trains runs at a speed of 54km/h , 36 wagons are attached to it.

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