a train covers a distance of 300km at a constant speed .if the speed of the train is increased by 5km/hr the journey would have taken 2 hour less.find the original speed of train?
If the original speed is $\displaystyle v \mbox{ km/hr}$, then the time to travel $\displaystyle 300 \mbox{ km}$ is:Originally Posted by anjana
$\displaystyle t_1=\frac{300}{v}\ \mbox{hr}$,
similarly at the higher speed it would take:
$\displaystyle t_2=\frac{300}{v+5}\ \mbox{hr}$.
But we are told $\displaystyle t_1=t_2+2 \mbox{ hr}$, so:
$\displaystyle
\frac{300}{v}=\frac{300}{v+5}+2
$
which we can rearrange to:
$\displaystyle
-2 v^2 + 10 v - 1500=0
$
Which has two solutions and you need the poitive one.
RonL