A man travels 600km partly by train and partly by car, it takes 8 houe and 40 minutes. If he travels 320km by train and the rest by car, it would take 30 minutes more if he travels 200km by train and the rest by car. Find the speed of the train and the car seperately.

Asked by Anjana S | 14th Jul, 2014, 05:33: PM

Expert Answer:

L e t space x space b e space t h e space s p e e d space o f space t h e space t r a i n space a n d space y space b e space t h e space s p e e d space o f space t h e space c a r. T o t a l space d i s tan c e space t r a v e l l e d space i s space 600 space k m. T h e space t i m e space t a k e n space b y space t h e space m a n space t o space t r a v e l space 320 space k m space b y space t r a i n space i s space 320 over x T h e space t i m e space t a k e n space b y space t h e space m a n space t o space t r a v e l space 280 space k m space b y c a r space i s space 280 over y H e n c e space t h e space t o t a l space t i m e space t a k e n space b y space t h e space m a n space t o space t r a v e l space 600 space k m space i s space 320 over x plus 280 over y G i v e n space t h a t space t h e space t o t a l space t i m e space i s space 8 space h o u r s space 40 space m i n u t e s equals 8 2 over 3 space h o u r s equals 26 over 3 space h o u r s T h u s comma space w e space h a v e comma space 320 over x plus 280 over y equals 26 over 3.... left parenthesis 1 right parenthesis T h e space t i m e space t a k e n space b y space t h e space m a n space t o space t r a v e l space 200 space k m space b y space t r a i n space i s space 200 over x T h e space t i m e space t a k e n space b y space t h e space m a n space t o space t r a v e l space 400 space k m space b y c a r space i s space 400 over y H e n c e space t h e space t o t a l space t i m e space t a k e n space b y space t h e space m a n space t o space t r a v e l space 600 space k m space i s space 200 over x plus 400 over y G i v e n space t h a t space t h e space t o t a l space t i m e space i s space 30 space m i n u t e s space m o r e space t h a n space 8 space h o u r s space 40 space m i n u t e s equals 8 2 over 3 space h o u r s plus 30 over 60 space h o u r equals 26 over 3 plus 1 half space h o u r s T h u s comma space w e space h a v e comma space 200 over x plus 400 over y equals 26 over 3 plus 1 half rightwards double arrow 200 over x plus 400 over y equals 55 over 6... left parenthesis 2 right parenthesis S u b s t i t u t e comma space 1 over x equals u space a n d space 1 over y equals v T h u s comma space e q u a t i o n s space left parenthesis 1 right parenthesis space a n d space left parenthesis 2 right parenthesis space c a n space b e space r e w r i t t e n space a s comma 320 u plus 280 v equals 26 over 3 200 u plus 400 v equals 55 over 6 S o l v i n g space t h e space a b o v e space e q u a t i o n s comma space w e space h a v e comma u equals 1 over 80 space a n d space v equals 1 over 60 T h u s comma space t h e space s p e e d s space o f space t h e space t r a i n space a n d space c a r space a r e space r e s p e c t i v e l y comma space 80 space k m divided by h o u r space a n d space 60 space k m divided by h o u r.

Answered by Vimala Ramamurthy | 15th Jul, 2014, 05:00: PM