a man travels 370 km partly …

Ans. Total Distance = 370 km

let speed of train= x  km/h

speed of car = y km/h

Case 1 : 

Distance travel by train = 250 km 

Time taken to cover this distance = {tex}({250\over x }) \ hour {/tex}

Distance travel by car = 370-250 = 120 km

Time Taken to cover this distance = {tex}({120\over y}) \ \ hour{/tex}

Total time = 4 hours

So,  {tex}{250\over x} + {120\over y} = 4 {/tex}

=> {tex}250y + 120x = 4xy {/tex}    ............... (1)

Case 2 :
Distance travel by train = 130 km 

Time taken to cover this distance = {tex}({130\over x }) \ hour {/tex}

Distance travel by car = 370-130 = 240 km

Time Taken to cover this distance = {tex}({240\over y}) \ \ hour{/tex}

Total time = 4 hours and 18 mintues = {tex}({43\over 10 }) \ hours{/tex}

So,  {tex}{130\over x} + {240\over y} = {43\over 10} {/tex}

=> {tex}1300y + 2400x = 43xy {/tex}    ............... (2)

Multilply eq(1) by 20, we get 

=> {tex}5000y + 2400x = 80 xy {/tex} .......... (3)

Subtract (2) from (3), we get 

=> 3700 y = 37xy

=> 37x = 3700

=> x = 100 

Put value of x in eq(1). we get 

=> 250y + 12000 = 400y

=> 12000 =  150y 

=> y = 80 

So Speed of train = 100 km/h

Speed of car = 80 km/h