Question

Train travels at a certain average speed for a distance of 63 km and then Travels a distance of 72 km at an average speed of 60 km per hour more than its original speed. If it takes 3 hours to complete the journey, then find its original average speed .

Answer 1

Correct Question :-

Train travels at a certain average speed for a distance of 63 km and then Travels a distance of 72 km at an average speed of 6 km per hour more than its original speed. If it takes 3 hours to complete the journey, then find its original average speed .

Solution :-

Let the -

• speed of train be x km/hr

The train travels at a certain average speed for a distance of 63 km.

Here -

• Distance of tain = 63 km
• Speed of train = x km/hr

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

$\implies\:\sf{\dfrac{63}{x}}$ hr.

Now, the train travels a distance of 72 km at an average speed of 6 km/hr more than its original speed.

Here -

• Distance = 72 km
• Speed = (x + 6) km/hr

$\implies\:\sf{\dfrac{72}{x\:+\:6}}$ hr.

According to question,

=> $\sf{\dfrac{63}{x}\:+\:\dfrac{72}{x\:+\:6}\:=\:3}$

=> $\sf{\dfrac{63(x+6)\:+\:72(x)}{x(x+6)}\:=\:3}$

=> $\sf{63x\:+\:378\:+\:72x\:=\:3(x^2\:+\:6x)}$

=> $\sf{135x\:+\:378\:=\:3x^2\:+\:18x}$

=> $\sf{3x^2\:-\:117x\:-\:378\:=\:0}$

=> $\sf{x^2\:-\:39x\:-\:126\:=\:0}$

=> $\sf{x^2\:-\:42x\:+\:3x\:-\:126\:=\:0}$

=> $\sf{x(x-42)\:+3(x-42)\:=\:0}$

=> $\sf{(x+3)\:(x-42)\:=\:0}$

=> $\sf{x\:=\:-3,\:42}$

(-3 neglected, as speed can't be negative)

•°• Speed of the train is 42 km/hr.

Answer 2

$\huge\underline\mathfrak\blue{Answer-}$

The original average speed of the train is 42 km/h.

$\huge\underline\mathfrak\blue{Explanation-}$

Refer to the attachment.