Question

A train travels at a certain average speed for a distance of $54km$ and then travels a distance of $63km$ at an average speed of $6km/h$ 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

Total time taken $=3hrs$

As $\frac{Distance}{Speed}=Time$

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

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

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

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

$\Rightarrow x^2-22x-108=0$

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

$x=36or-3$

$x=-3$ is not admissible

Hence, its first speed is 36 kmph.