Question

The distance between two towns is $20km$ less by road than by rail. A train takes three hours for the journey, a car four hours. If the average speed of the car is $15km/hr$ less than that of the train what is the average speeds of the car?

• A. $40km/hr$
• B. $35km/hr$
• C. $25km/hr$
• D. $50km/hr$

Answer 1

The correct option is C $25km/hr$

Let the distance between the two town by road be $xkm$
$\therefore$ distance by train is $(x+20)km$
Average speed of car be $ykm/h$
$\therefore$ Average speed of train is $(y+15)km/h$.
Given,
$y=\frac{x}{4}$ $\left(i\right)$
$y+15=\frac{x+20}{3}$ $\left(ii\right)$
$\Rightarrow 3y+45=x+20$
$\Rightarrow 3y-x=20-45$
$\Rightarrow 3\left(\frac{x}{4}\right)-x=-25$ [Putting the value of $y$ from equation $\left(i\right)$]
$\Rightarrow \frac{3x}{4}-x=-25$
$\Rightarrow \frac{3x-4x}{4}=-25$
$=>-x=-100$
$=>x=100$
Putting the value in equation $\left(i\right)$, we get,
$y=\frac{x}{4}$
$\Rightarrow y=\frac{100}{4}$
$\Rightarrow y=25$
$\therefore$ Average speed of the car is $25km/h$