Question

a train travels a distance of 480 km at a uniform speed .if the speed had been 8km/h less then it would have taken 3 hours more to cover the same distance .we need to 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 was 8 km/hr less, it would have taken 3 more hours to cover the distance

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

• The speed of the train

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

→ Let the speed of the train be x km/hr

→ Decrease in speed = (x - 8) km/hr

→ We know that,

  Time = Distance/Speed,

→ By given,

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

→ Cross multiplying we get,

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

   $\sf{\dfrac{480x-480x+3840}{x^{2} -8x} =3}$

  3x² - 24x - 3840 = 0

→ Divide the whole equation by 3

  x² - 8x - 1280 = 0

→ Solving the quadratic equation by splitting the middle term

   x²- 40x + 32x - 1280 = 0

→ Taking the common factors out,

  x (x - 40) + 32 (x - 40) = 0

→ Taking x - 40 as common

  (x - 40) × (x + 32) = 0

→ First case,

  x + 32 = 0

  x = -32

→ This can't happen as speed can't be negative

→ Second case,

  x - 40 = 0

  x = 40

→ Hence 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

• Factorization method
• Splitting the middle term
• Completing the square method