CBSE Class 10 Answered

can you please explain me the system of upstream and downstream with a sample word problem.

Asked by Sanmit Ratnaparkhi | 08 Jul, 2014, 10:32: PM

Expert Answer

$C o n s i d e r space t h e space f o l l o w i n g space q u e s t i o n space o n space u p s t r e a m space a n d space d o w n s t r e a m. Q u e s t i o n : A space b o a t space g o e s space 24 space k m space u p s t r e a m space a n d space 28 space k m space d o w n s t r e a m space i n space 6 space h o u r s. space I t space g o e s space 30 space k m space u p s t r e a m space a n d space 21 space k m space d o w n s t r e a m space i n space 6 1 half space h o u r s. space F i n d space t h e space s p e e d space o f space t h e space b o a t space i n space s t i l l space w a t e r space a n d space a l s o space s p e e d space o f space t h e space s t r e a m. S o l u t i o n : 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 b o a t space i n space s t i l l space w a t e r space a n d space l e t space y space b e t space t h e space s p e e d space o f space t h e space s t r e a m space b e space y space k m divided by h r. T h u s comma space t h e space s p e e d space o f space u p s r e a m space i s space open parentheses x minus y close parentheses space k m divided by h r a n d space t h e space s p e e d space o f space d o w n s t r e a m space i s space open parentheses x plus y close parentheses space k m divided by h r T i m e space t a k e n space t o space c o v e r space 24 space k m space u p s t r e a m space equals fraction numerator 24 over denominator x minus y end fraction h o u r s T i m e space t a k e n space t o space c o v e r space 28 space k m space d o w n s t r e a m space equals fraction numerator 28 over denominator x plus y end fraction h o u r s 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 o f space t r a v e l l i n g space i s space 6 space h o u r s. T h e r e f o r e comma space w e space h a v e comma space fraction numerator 24 over denominator x minus y end fraction plus fraction numerator 28 over denominator x plus y end fraction equals 6 S i m i l a r l y comma space T i m e space t a k e n space t o space c o v e r space 30 space k m space u p s t r e a m space equals fraction numerator 30 over denominator x minus y end fraction h o u r s T i m e space t a k e n space t o space c o v e r space 21 space k m space d o w n s t r e a m space equals fraction numerator 21 over denominator x plus y end fraction h o u r s 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 o f space t r a v e l l i n g space i s space 6 space h o u r s. T h e r e f o r e comma space w e space h a v e comma space fraction numerator 30 over denominator x minus y end fraction plus fraction numerator 21 over denominator x plus y end fraction equals 6 1 half rightwards double arrow fraction numerator 30 over denominator x minus y end fraction plus fraction numerator 21 over denominator x plus y end fraction equals 13 over 2 T h u s comma space w e space h a v e space t h e space s y s t e m space o f space e q u a t i o n s comma space fraction numerator 24 over denominator x minus y end fraction plus fraction numerator 28 over denominator x plus y end fraction equals 6.... left parenthesis 1 right parenthesis a n d fraction numerator 30 over denominator x minus y end fraction plus fraction numerator 21 over denominator x plus y end fraction equals 13 over 2... left parenthesis 2 right parenthesis N o w space s u b s t i t u t e space fraction numerator 1 over denominator x minus y end fraction equals u space a n d space fraction numerator 1 over denominator x plus y end fraction equals v space i n 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 24 u plus 28 v equals 6.... left parenthesis 3 right parenthesis a n d 30 u plus 21 v equals 13 over 2... left parenthesis 4 right parenthesis S o l v i n g space e q u a t i o n s space left parenthesis 3 right parenthesis space a n d space left parenthesis 4 right parenthesis comma space w e space h a v e u equals 1 over 6 space a n d space v equals 1 over 14 T h u s comma space w e space h a v e comma fraction numerator 1 over denominator x minus y end fraction equals u space a n d space fraction numerator 1 over denominator x plus y end fraction equals v rightwards double arrow x minus y equals 6 space a n d space x plus y equals 14 S o l v i n g space t h e space a b o v e space t w o space e q u a t i o n s space w e space h a v e x equals 10 space k m divided by h o u r space a n d space y equals 4 space k m divided by h o u r T h u s comma space t h e space s p e e d space o f space t h e space b o a t space i n space s t i l l space w a t e r space i s space 10 space k m divided by h o u r space a n d space t h e space s p e e d space o f space t h e space s t r e a m space i s space 4 space k m divided by h o u r$