Question

A train travels at a certain average speed for a distance of 54 km and then travels a distance of 63 km at an average speed of 6 km/h more than the first speed. If it takes 3 hours to complete the total journey, what is its first speed?

Answer 1

Distance $=54km$

Let the average speed be $x$

Distance $=63km$

The average speed to cover this distance $=x+6$

Total time taken $=3hr$

$t=\frac{D}{S}$

$\therefore \frac{54}{x}+\frac{63}{x+6}=3$

$\Rightarrow \frac{54(x+6)+63x}{x(x+6)}=3$

$\Rightarrow 54x+324+63x=3x^2+18x$

$\Rightarrow 3x^2-99x-324=0$

$\Rightarrow x^2-33x-108=0$

$\Rightarrow x^2-36x+3x-108=0$

$\Rightarrow x(x-36)+3(x-36)=0$

$\Rightarrow (x-36)(x+3)=0$

Then $x=36$ and $x=-3$

$x=-3$ is not admissible because it is negative

Then $x=36$

So speed $=36km/hr$