3 years from now will be 360. We would like I THU
(iv) A train travels a distance of 480 km at a uniform speed. If the speed

Question

3 years from now will be 360. We would like I THU
(iv) A train travels a distance of 480 km at a uniform speed. If the speed had been
8 km/h less, then it would have taken 3 hours more to cover the same distance. We
need to find the speed of the train. a quadratic equation for this??? ​

in progress 0
Jasmine 1 year 2021-07-15T15:22:51+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-07-15T15:23:55+00:00

    Answer

    Let the speed of the train be x km/hr. Then

    Time taken to travel a distance of 480km=

    x

    480

    hr

    Time taken by the train to travel a distance of 480km with the speed (x−8)km/hr=

    x−8

    480

    hr

    It is given that if the speed had been 8km/hr less, then the train would have taken 3 hours more to cover the same distance

    x−8

    480

    =

    x

    480

    +3

    x−8

    480

    x

    480

    =3⇒

    x(x−8)

    480(x−x+8)

    =3⇒

    x(x−8)

    480×8

    =3

    ⇒3x(x−8)=480×8⇒x(x−8)=160×8⇒x

    2

    −8x−1280=0

    This is the required quadratic equation.

    0
    2021-07-15T15:24:20+00:00

    : ANSWER

    The speed of train is = 40 km /hr

    : GIVEN

    Distance covered = 480 km

    if the speed has been 8 km / hr less

    : FIND

    Speed of the train

    : SOLUTION

     \looparrowrightLet the normal speed be x km \hr

     \looparrowright We know that

     \looparrowright Time = Distance/ speed

    \mapsto  \frac{480}{x - 8}  -  \frac{480}{x}  = 3[tex]\mapsto[/tex] Cross multiplying

     \frac{480x - 480(x - 8)}{x(x - 8)}  = 3[tex]\mapsto[/tex] 480x – 480x + 3840=3(x2- 8x)

    \mapsto 3x {}^{2}  - 24x - 3840 = 0

     \looparrowright Factories by splitting the middle term

    \mapsto x {}^{2}  - 40x + 32x - 1280 = 0

    \mapsto x(x - 40) + 32(x - 40) = 0

    \mapsto (x - 40)(x + 32) = 0

    \mapsto x =  - 32 \: x = 40

     \looparrowright Here speed can’t be negative

     \implies So, the train speed is 40 km /hr

     \sf \boxed{speed \: of \: the \: train \: is = 40 \: km \ \:hr}

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