Question

A passenger train takes $2$ hours more than an express train to travel a distance of $240km$. The speed of the express train is more than that of passenger train by $20km/h$. Find the speed of both the trains.

Answer 1

Velocity of passenger train=$V_p$

Velocity of express train=$V_e$

Time taken by passenger train =$t_p$

Time taken by express train =$t_e$

Distance traveled, $s=V_p{t}_p=V_e{t}_e=240km$

$240=V_p{t}_p=(V_p+20)(t_p-2)$

$240=V_p{t}_p=V_p{t}_p-2V_p+20t_p-40$

$240=-2V_p+20\left(\frac{240}{V_p}\right)-40$

$240V_p=-2V_p^2+4800-40V_p$

$-2V_p^2-280V_p+4800=0$

$2V_p^2+280V_p-4800=0$

$V_p^2+140V_p-2400=0$

$V_p=\frac{-140\pm \sqrt{{140}^2+4\times 2400}}{2}$

$V_p=15.44km/h$ (speed cannot be negative)

$V_e=V_p+20=35.44km/h$