Question

Hardish travels $600$ km partly by train and partly by car. If she covers $120\text{km}$ by train and rest by car, it takes her $8$ hours. But if she travels $200\text{km}$ by train and rest by car, she takes $20$ minutes more. Find the speed of the train and car separately.

Answer 1

Let $V_1$ be speed of train, $V_2$ be speed of car.

$\frac{120}{V_1}+\frac{480}{V_2}=480$

$\frac{200}{V_1}+\frac{400}{V_2}=500$

$120x+480y=480$ $[x=\frac{1}{V_1},y=\frac{1}{V_2}]$

$200x+400y=500$

$\Rightarrow x=1,y=3/4$

$\Rightarrow V_1=1km/min{V}_2=4/3km/min$

$=60km/hr$ $=80km/hr$

$\therefore$ Speed of train $=60km/hr$

Speed of car $=80km/hr$