Question

A train travels a distance of 480 km at a uniform speed. If the speed had been
need to find the speed of the train.
8 km/h less, then it would have taken 3 hours more to cover the same distance. We​

Answer 1

Answer:

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. But speed of the train cannot be –ve. x = 40.

Answer 2

Step-by-step explanation:

Correct Question:-

A train travels a distance of 480km 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.

$\bf{\underline{\underline\red{Given:-}}}$

• Distance = 480km

• If speed is decreased by 8km/h, it would take 3hours more to cover the same distance.

$\bf{\underline{\underline\blue{To\:Find:-}}}$

• The speed of the train.

$\bf{\underline{\underline\green{Solution:-}}}$

Given, Distance = 480km

Let the speed be x km/h

$\boxed{ \rm \leadsto Time = \frac{Distance}{Speed} }$

${ \rm \implies Time = \dfrac{480}{x} \: hrs }$

$\rm If\: speed\: is \:decreased \:by \:8km/h$

$\rm Speed = (x-8)km/hr$

$\rm As\: distance\: is \:same$

$\rm Distance = 480km$

$\rm Time = \dfrac{480}{x-8}$

Given, if speed is decreased by 8km/h, time taken is 3 hours more

${ \rm \implies \dfrac{480}{x - 8} = \dfrac{480}{x} + 3 }$

${ \rm \implies \dfrac{480}{x - 8} - \dfrac{480}{x} = 3 }$

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

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

${ \rm \implies { 3840} = 3 ( {x}^{2} - 8x)}$

${ \rm \implies \dfrac { 3840} {3} = {x}^{2} - 8x}$

${ \rm \implies 1280 = {x}^{2} - 8x}$

${ \rm \implies {x}^{2} - 8x - 1280 = 0}$

${ \rm \implies {x}^{2} - 40x + 32x - 1280 = 0}$

${ \rm \implies {x}(x - 40) + 32(x - 40) = 0}$

${ \rm \implies (x - 40)(x + 32) = 0}$

${ \rm \implies x - 40 = 0 \: \: \: (or )\: \: \: x + 32= 0}$

${ \rm \implies x = 40 \: , \: - 32}$

Since, speed of the train cannot be negative

${ \rm \implies x = 40 }$

$\underline {\boxed{ \rm \purple{ \therefore Speed \: of \: the \: train = 40km/h}}}$