Question

A journey of 600 km. Due to some problem in Vehicle speed was reduced to 200 kmph and it takes 30min extra, Find the Actual time taken for Journey​

Answer 1

Answer:

the original speed will be 240kmph

Answer 2

$\large\underline{\sf{Solution-}}$

Let assume that the original speed be x km per hour.

Case :- 1

Distance covered = 600 km

Speed of journey = x km per hour.

We know,

$\boxed{ \sf{ \:Time = \frac{Distance}{Speed}}}$

So,

Time taken to travel 600 km at a speed of x km per hour is

$\rm :\longmapsto\:t_1 = \dfrac{600}{x} - - - - (1)$

Case :- 2

Distance covered = 600 km

Speed of journey = x - 200 km per hour.

We know,

$\boxed{ \sf{ \:Time = \frac{Distance}{Speed}}}$

So,

Time taken to travel 600 km at a speed of x - 200 km per hour is

$\rm :\longmapsto\:t_2 = \dfrac{600}{x - 200} - - - - (2)$

According to statement,

$\rm :\longmapsto\:t_2 - t_1 = \dfrac{1}{2}$

$\rm :\longmapsto\:\dfrac{600}{x - 200} - \dfrac{600}{x} = \dfrac{1}{2}$

$\rm :\longmapsto\:\dfrac{600x - 600(x - 200)}{(x - 200)x} = \dfrac{1}{2}$

$\rm :\longmapsto\:\dfrac{600x - 600x + 120000}{(x - 200)x} = \dfrac{1}{2}$

$\rm :\longmapsto\:\dfrac{120000}{ {x}^{2} - 200x} = \dfrac{1}{2}$

$\rm :\longmapsto\: {x}^{2} - 200x = 240000$

$\rm :\longmapsto\: {x}^{2} - 200x - 240000 = 0$

$\rm :\longmapsto\: {x}^{2} - 600x + 400x - 240000 = 0$

$\rm :\longmapsto\:x(x - 600) + 400(x - 600) = 0$

$\rm :\longmapsto\:(x - 600)(x + 200) = 0$

$\bf\implies \:x = 600 \: \: \: or \: \: \: x = - \: 400$

$\bf\implies \:x \: = \: 600 \: km \: per \: hour$

So, time taken for journey is

$\rm :\longmapsto\:t_1 = \dfrac{600}{600}$

$\bf\implies \:t_1 = 1 \: hour$

Additional Information :-

Concept Used :-

Let us consider a quadratic equation ax² + bx + c = 0, then nature of roots of quadratic equation depends upon Discriminant (D) of the quadratic equation.

If Discriminant, D > 0, then roots of the equation are real and unequal.

If Discriminant, D = 0, then roots of the equation are real and equal.

If Discriminant, D < 0, then roots of the equation are unreal or complex or imaginary.

Where,

Discriminant, D = b² - 4ac