Question

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. Find the speed of the train.​

Answer 1

Answer:

$\bigstar{\bold{Speed\:of\:the\:train=40\:km/hr}}$

Step-by-step explanation:

$\Large{\underline{\underline{\bf{Given:}}}}$

• Distance covered = 480 km
• If the speed has been 8 km/hr less, it would have taken 3 more hours

$\Large{\underline{\underline{\bf{To\:Find:}}}}$

• Speed of the train

$\Large{\underline{\underline{\bf{Solution:}}}}$

➝ Here we are given that the train covers the distance of 480 km at a uniform speed.

➝ Let the normal speed be x km/hr

➝ Hence,

    Decrease in speed = (x - 8) km/hr

➝ Now we know that,

    Time = Distance/Speed

➝ Hence by given

    $\sf{\dfrac{480}{x-8}-\dfrac{480}{x}=3}$

➝ Cross multiplying,

    $\sf{\dfrac{480x-480(x-8)}{x(x-8)}=3}$

    480x - 480x + 3840 = 3(x² - 8x)

     3x² - 24x - 3840 = 0

➝ Dividing the whole equation by 3

    x² - 8x - 1280 = 0

➝ Factorising by splitting the middle term,

    x² - 40x + 32x - 1280 = 0

    x (x - 40) + 32 (x - 40) = 0

    (x - 40) (x + 32) = 0

     x = -32, x = 40

➝ Here speed can't be negative

➝ So the speed of the train is 40 km/hr

    $\boxed{\bold{Speed\:of\:the\:train=40\:km/hr}}$

$\Large{\underline{\underline{\bf{Notes:}}}}$

➝ A quadratic equation can be solved by

• Quadratic formula
• Splitting the middle term
• Completing the square