Question

An express train takes $2$ hour less time than a passenger train to travel $400km$ between two stations (without taking into consideration the time they stop at intermediate stations). If the average speed of the express train is $10km/h$ more than of the passenger train, find the average speed of the two trains

Answer 1

Let the speed of express train be $xkm/h$

Let the speed of passenger train be $ykm/h$

$x=y+10..........\left(i\right)$

Time is defined as the ratio of distance to speed.

Time of express train is less than passenger train by $2h$

$\frac{400}{x}+2=\frac{400}{y}...........\left(ii\right)$

Substituting value of $x$ from (i) in (ii), we get:

$\frac{400}{y+10}+2=\frac{400}{y}$

Rearranging terms, we get:

$y^2+10y-2000=0$

$\Rightarrow y^2+50y-40y-2000=0$

$\Rightarrow (y+50)(y-40)=0$

$\Rightarrow y=-50ory=40$

Speed cannot be negative, therefore

$y=40$

From equation (i),

$x=y+10=50$

Hence,

average speed of express train is $50km/h$

average speed of passenger train is $40km/h$