Question

A train travels $360km$ at a uniform speed. If the speed had been $5km/h$ more, it would have been taken $1$ hours less for the same journey. Find the speed of the train.

Answer 1

Let the speed of the train $=v$

$time=\frac{distance}{speed}$

in a case $1$

$time\left(t\right)=360/v$

in case $2$

$time\left(T\right)=360/v+5$

As,

$t-T=1$

So,

$\frac{360}{v}-\frac{360}{v+5}=1$

$360\left(\frac{v+5-v}{v\left(v+5\right)}\right)=1$

$360\left(5\right)=v\left(v+5\right)$

$v^2+5v-1800=0$

$v^2+45v-40v-1800=0$

$\left(v+45\right)\left(v-40\right)=0$

$v=-45,40$

As speed cannot be negative,

Thus a speed of the train is 40$km/h{r}^2$