Question

A train travels 360 km at a uniform speed. If the speed had been 5 km /hr more, it would have taken 1 hour less for the same journey. Form the quadratic equation to find the speed of the train.

Answer 1

Given,

Distance $=360$ km
Let the speed be $x$, then time taken

$t=\frac{360}{x}$
If speed is increased by 5 km/h speed will be $(x+5)$km/h
Distance is the same
$t=\frac{360}{(x+5)}$

time with original speed - time with increased speed $=1$
therefore,
$\frac{360}{x}-\frac{360}{(x+5)}=1$
$LCM=x(x+5)$
Hence,

$\frac{360(x+5)-360x}{x(x+5)}=1$
$360x+1800-360x=x(x+5)$
$x^2+5x=1800$
$x^2+5x-1800=0$
$x^2+45x-40x-1800=0$
$x(x+45)-40(x+45)=0$
$(x-40)(x+45)=0$
$x=40\frac{km}{hr}$,

So the speed of the train is 40 km/hr. We have discarded the other value as the negative value of speed $(-45)$ is not possible.