Question

A train travels a distance of 480 km at a uniform speed. If the speed had been 40 km/h less, then it would have taken 4 hours more to cover the same distance. Find the speed of the train.

Answer 1

Let the speed of the train be $x$

The distance covered is $450km$

So the time taken is $\frac{450}{x}\cdots \left(1\right)$

The speed is now $40kmph$ less, so the speed is $x-40$

The same distance so $450km$

Time taken is $\frac{450}{x-40}$

According to question,

The second case takes $4$ more hours to reach a destination

So $\frac{450}{x}=\frac{450}{x-40}+4$

$\frac{450}{x}=\frac{450}{x-40}+\frac{4(x-40)}{x-40}$

$450(x-40)=450\left(x\right)+4x(x-40)$

$4x^2-160x-4500=0$

$x^2-40x-4500=0$

$x^2-90x+50x-4500=0$

$x(x-90)+50(x-90)=0$

$(x-90)(x+50)=0$

$x=90,-50$

Speed cannot be negative so the speed of the train is $90kmph$