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:
Answer & explanation
Correct answer: option 4
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