A person travels a distance of 240 km, partly by train and the rest by bus.He takes 3 1$$\frac{1}{2}$$ hours if he travels 150 km by the train and the rest by bus.If he travels 140 km by bus and rest by train .He takes 3 $$\frac{2}{3}$$. What is the Speed of the tarin?

Let speed of train = $$x$$ km/hr

and speed of bus = $$y$$  km/hr

according to question $$ \dfrac{150}{x} + \dfrac{90}{y} = \dfrac{7}{2} $$ ............ equestion (1)

 (where total distance 240 -150 = 90 km travel by bus ,total time taken = $$ 3\dfrac{1}{2}$$)

again $$\dfrac {100}{x} + \dfrac{140}{y} = \dfrac{11}{3} $$  ............equestion (2)

we multiply by equesion(1) by 2 and  equestion (2 )multiply by 3 

then substract eqestion (2)from (1) we find that

$$\dfrac{180-420}{y} = -4 $$

$$\Rightarrow y = \dfrac{-240}{-4}$$

$$\Rightarrow y = 60$$

put y = 60 in equestion (1)

then $$\dfrac {150}{x}+ \dfrac{90}{60} = \dfrac {7}{2}$$ 

$$\Rightarrow x = \dfrac{150}{2}$$

$$\Rightarrow x = 75 $$ km/ hr Ans