Question 32114
Let the spped of the train be x km/hr and that of the car is y km/hr
Time taken to travel 120 km by train and 480 km by car is 120/x + 480/y
Per question, 120/x + 480/y = 8
=>15/x + 60/y=1
=>15y+60x=xy....... (Eq 1)
Time taken to travel 200 km by train and 400 km by car is 200/x + 400/y
Per question, 200/x + 400/y = 8 1/3=25/3
=> 8/x + 16/y = 1/3
=> 24y+48x=xy....... (Eq 2)
From both equations:
15y+60x = 24y+48x
=>9y=12x
=>y=4x/3
Substituting this in (Eq 1)
15y+60x=xy
=>20x+60x=4x^2/3
=> 80x=4x^2/3
=>x^2-60x=0
=>x=60 (because speed Cannot be negative)
y=80
The speed of the train is 60 km/hr and the speed of the car is 80 km/hr