Question

A train covered a certain distance at a uniform speed. If the train would have been 6 km/h faster, it would have taken 4 hours less than the scheduled time. And, if the train were slower by 6 km/h, it would have taken 6 hours more than the scheduled time. Find the length of the journey

• A. None of these
• B. 840 km
• C. 880 km
• D. 720 km

Answer 1

Answer: (D)

Let the length of the journey be x km.

And uniform speed be y km/hr.

$\therefore$ scheduled time of journey$=\frac{x}{y}hours$

As per question,

$\frac{x}{y}=\frac{x}{(y+6)}+4..\left(i\right)$

$\frac{x}{y}=\frac{x}{(y-6)}-6..\left(ii\right)$

From eq 1

$\Rightarrow \frac{x}{y}=\frac{x+4y+24}{y+6}$

$\Rightarrow xy+6x=xy+4y^2+24y$

$\Rightarrow 6x=4y^2+24y...\left(iii\right)$

From eq 2

$\frac{x}{y}=\frac{x-6y+36}{(y-6)}$

$\Rightarrow xy-6x=xy-6y^2+36y$

$\Rightarrow -6x=-6y^2+36y....\left(iv\right)$

$\because 4y^2+24y=6y^2-36y$

$\Rightarrow 2y^2=60y$

$\Rightarrow y=\frac{60}{2}=30$

From eq3

$\Rightarrow x=\frac{4y^2+2y}{6}$

$\Rightarrow x=\frac{4\times 900+24\times 30}{6}$

$\Rightarrow x=720km.$

Hence the length of the journey $=720km$