The speed of a train is 3 times that of a car and 1.5 times that of a steamer. A person travelled by x km by steamer, 3.75 x km by train and $\frac{x}{2}$ km by car. If the speed of the car is 40 km/h and total time take by him is $4\frac{1}{2}$ hours, then the total distance traveled by him in three modes is:

420 km

Speed of car = 40 km/h

So , Speed of train = 3 × 40 = 120 km/h

Speed of streamer = \(\frac{120}{1.5}\) = 80 km/h

Let distance traveled by Streamer = D km

According to question ,

\(\frac{D}{80}\) + \(\frac{3.75× D}{120}\) + \(\frac{ D}{2 ×40  }\) = \(\frac{9}{2}\)

13.5  × D = \(\frac{9}{2}\) × 240

D = 80 km

So , Distance = D + 3.75D + \(\frac{D}{2}\)

= 5.25 ×80 = 420 km