Question

If a train travelled 3 km/hr slower, it would take one hour more to travel a distance of 6 km. The speed of train is .

• A. 6 km/hr
• B. 3 km/hr
• C. 2 km/hr

Answer 1

The correct option is A 6 km/hr

Let the speed of the train be $x$ km/hr.
Total distance travelled = 6 km

$\Rightarrow$ Time taken by the train to travel 6 km = $\frac{6}{x}$ hours

When the speed is slowed down by 3 km/hr, the new speed is $(x-3)$ km/hr.

$\Rightarrow$ Time taken to travel 6 km with the new speed is $\frac{6}{x-3}$ hours.

From the given condition,
$\frac{6}{x-3}-\frac{6}{x}=1.$

$\frac{6x-6(x-3)}{x(x-3)}=1$

$\Rightarrow 18=x(x-3)$

$\Rightarrow 18=x^2-3x$

$\Rightarrow x^2-3x-18=0$

$\Rightarrow x^2-6x+3x-18=0$

$\Rightarrow x(x-6)+3(x-6)=0$

$\Rightarrow (x+3)(x-6)=0$

$\Rightarrow x=-3,6$

Since speed can not be negative, we have $x=6$ km/hr.

Thus, the speed of train is 6 km/hr.