A fast train takes 3 hours less than a slow train for a journey of 600 km. If the speed of slow train is 10 km / hr less than that of the fast train, find the speeds of the two trains. 

Asked by arindeep.singh | 29th May, 2020, 03:14: PM

Expert Answer:

L e t space t h e space s p e e d space o f space t h e space s l o w space t r a i n space b e space x space k m divided by h r therefore S p e e d space o f space t h e space f a s t space t r a i n space equals space left parenthesis x plus 10 right parenthesis space k m divided by h r T i m e space t a k e n space b y space s l o w space t r a i n space equals space 600 over x T i m e space t a k e n space b y space f a s t space t r a i n space equals space fraction numerator 600 over denominator left parenthesis x plus 10 right parenthesis end fraction T i m e space t a k e n space b y space s l o w space t r a i n space minus space t i m e space t a k e n space b y space f a s t space t r a i n space equals space 3 rightwards double arrow 600 over x minus fraction numerator 600 over denominator left parenthesis x plus 10 right parenthesis end fraction equals 3 rightwards double arrow fraction numerator 600 x plus 6000 minus 600 x over denominator x left parenthesis x plus 10 right parenthesis end fraction equals 3 rightwards double arrow fraction numerator 6000 over denominator x left parenthesis x plus 10 right parenthesis end fraction equals 3 rightwards double arrow fraction numerator 2000 over denominator x left parenthesis x plus 10 right parenthesis end fraction equals 1 rightwards double arrow 2000 equals x squared plus 10 x rightwards double arrow x squared plus 10 x minus 2000 equals 0 rightwards double arrow x squared plus left parenthesis 50 minus 40 right parenthesis x minus 2000 equals 0 rightwards double arrow x squared plus 50 x minus 40 x minus 2000 equals 0 rightwards double arrow x left parenthesis x plus 50 right parenthesis minus 40 left parenthesis x plus 50 right parenthesis equals 0 rightwards double arrow left parenthesis x minus 40 right parenthesis left parenthesis x plus 50 right parenthesis equals 0 therefore space x equals space 40 comma space minus 50 S p e e d space o f space t h e space s l o w space t r a i n space equals space 40 space k m divided by h r S p e e d space o f space t h e space f a s t space t r a i n space equals space 50 space k m divided by h r

Answered by Renu Varma | 29th May, 2020, 05:57: PM