Two cars travel from city A to city B at a speed of 36 and 54 km/hr respectively. If one car takes 3.5 hours lesser time than the other car for the journey, then the distance between City A and City B is

Let the distance between City A and City B = $$d$$ km

Speed of first car = 36 km/hr and speed of second car = 54 km/hr

Let time taken by first car = $$t$$ hrs and time taken by second car = $$(t - 3.5)$$ hrs

Using, speed = distance/time for first car :

=> $$\frac{d}{t} = 36$$

=> $$d = 36t$$ --------------(i)

For second car, => $$\frac{d}{t - 3.5} = 54$$

Substituting value of $$d$$ from equation (i), we get :

=> $$36t = 54t - 189$$

=> $$54t - 36t = 18t = 189$$

=> $$t = \frac{189}{18} = \frac{21}{2}$$ hrs

From equation (i), => $$d = 36 \times \frac{21}{2} = 378$$ km

=> Ans - (D)