On a journey of 600 km, a train was delayed 1 hour and 30 min after having covered 1 4 of the way. To arrive on time at the destination, the

Question

On a journey of 600 km, a train was delayed 1 hour and 30 min after having covered 1 4 of the way. To arrive on time at the destination, the engine driver had to increase the speed by 15 km/hour. How long did the train travel for

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Calantha 5 months 2021-08-30T14:16:47+00:00 1 Answers 1 views 0

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    2021-08-30T14:17:52+00:00

    Answer:

    The train travelled 10hours.

    Explanation:

    Using speed= distance/time …eq1

    Let the time taken by train to cover the journey be t.

    Let the speed of train be s

    Time= distance/speed …eq2

    Time t =600/s …eq3

    The train is delayed for 1 1/2 hours=3/2 hours

    Train increased by 15km/hr.

    Train travelled 1/4 of 600k.= 150km.

    Speed increased by s + 15 to cover the remaining 450km

    t = 150/s + 400/(s + 15) + 3/2 ..eq4

    Equating eq3 and 4

    600/s= 150/s + 460/(s + 15) + 3/2

    450/s = 3/2 + 450/(s + 15)

    3s^2 + 45s -13500=0

    Solving the quadratic equation

    S= -45 +-sqrt(45^2-4(3×13500)/2×3

    S= 60 , -75

    Hence speed of train is 60km/hr

    Using eq 2 distance/speed=time

    600/60=10

    t= 10hours

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