A train covers a certain distance at a uniform speed . On increasing its speed by 5 km/hr it saves 20 minutes and on decreasing its speed by

Question

A train covers a certain distance at a uniform speed . On increasing its speed by 5 km/hr it saves 20 minutes and on decreasing its speed by 20 km/hr it loses 2 hrs. Find the distance covered by the train

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Isabella 3 months 2021-11-06T17:46:00+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-11-06T17:47:17+00:00

    Step-by-step explanation:

    Let the speed of the train be xkm/h and the time taken by train to travel the given distance be t hours and the distance to travel be dkm. We know that,

    ⇒Speed=

    Time

    Distance

    ⇒x=

    t

    d

    ∴d=xt…….(i)

    Case 1

    ⇒(x+10)×(t−2)=d

    ⇒xt+10t−2x−20=d

    ⇒d+10t−2x−20=d

    ⇒−2x+10t=20…… (ii)

    Case 2

    ⇒(x−10)×(t+3)=d

    ⇒xt−10t+3x−30=d

    ⇒d−10t+3x−30=d

    ⇒3x−10t=30……… (iii)

    Adding equations (ii) and (iii), we gets

    ⇒x=50

    Substitute the value of x in (ii) we gets

    ⇒(−2)×(50)+10t=20

    ⇒−100+10t=20

    ⇒10t=120

    ⇒t=12 hours

    Substitue the value of t and x in equation (i), we gets

    Distance to travel =d=xt

    ⇒d=12×50=600Km

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

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    0
    2021-11-06T17:47:25+00:00

    Answer:

    Step-by-step explanation:

    Answer:

    Let us consider


    Time is taken = t

    Speed = x


    Distance = d


    Time = Distance/Speed


    or


    Speed = Distance/time


    x = d/t


    d = xt………………………………….(1)


    Case 1:


    d = (x + 10)(t – 2)


    d = xt – 2x +10t -20


    d = d – 2x +10t -20 [from (1) xt = d]


    10t – 2x = 20…………………………………..(2)


    Case2:


    d = (x – 10)(t + 3)


    d = xt + 3x -10t – 30


    d = d + 3x -10t – 30 [from (1) xt = d]


    3x -10t = 30…………………………………..(3)


    Adding equation (2) and (3)


    (10t – 2x + 3x -10t) = 20 + 30


    x = 50


    Substituting the value of x in 2


    10t – 2 × 50 = 20


    10t = 100 + 20


    10t = 120


    t = 12 hours


    Now substitute the value of t and in x in equation (1)


    Distance d = xt


    d = 50 × 12


    d = 600 km


    Therefore distance covered by the train is 600km.

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