the speed of a boat in still water is 8km/hr. it can go 15km upstream and 22km downstream in 5hrs. find the speed of the stream.

Asked by Akansha | 2nd Jul, 2014, 10:11: 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 s t r e a m. S p e e d space o f space t h e space b o a t space i n space space s t i l l space w a t e r space i s space 8 space k m divided by h r. T h u s 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 u p s t r e a m space i s space 8 minus x space k m divided by h r. A 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 d o w n s t r e a m space i s space 8 plus x space k m divided by h r. W e space k n o w space t h a t space T i m e equals fraction numerator D i s tan c e over denominator S p e e d end fraction T h e space t i m e space t a k e n space b y space t h e space b o a t space t o space c o v e r space 15 space k m space equals fraction numerator 15 over denominator 8 minus x end fraction space h o u r T h e space t i m e space t a k e n space b y space t h e space b o a t space t o space c o v e r space 22 space k m space equals fraction numerator 22 over denominator 8 plus x end fraction space h o u r T h e space t o t a l space t i m e space equals 5 space h o u r s space open square brackets g i v e n close square brackets rightwards double arrow fraction numerator 15 over denominator 8 minus x end fraction plus fraction numerator 22 over denominator 8 plus x end fraction equals 5 rightwards double arrow 15 open parentheses 8 plus x close parentheses plus 22 open parentheses 8 minus x close parentheses equals 5 open parentheses 8 minus x close parentheses open parentheses 8 plus x close parentheses rightwards double arrow 120 plus 15 x plus 176 minus 22 x equals 5 open parentheses 64 minus x squared close parentheses rightwards double arrow 296 minus 7 x equals 320 minus 5 x squared rightwards double arrow 5 x squared minus 7 x minus 24 equals 0 rightwards double arrow 5 x squared minus 15 x plus 8 x minus 24 equals 0 rightwards double arrow 5 x open parentheses x minus 3 close parentheses plus 8 open parentheses x minus 3 close parentheses equals 0 rightwards double arrow open parentheses 5 x plus 8 close parentheses open parentheses x minus 3 close parentheses equals 0 rightwards double arrow 5 x plus 8 equals 0 space o r space x minus 3 equals 0 rightwards double arrow x equals fraction numerator minus 8 over denominator 5 end fraction equals 0 space o r space x equals 3 space rightwards double arrow x equals 3 space sin c e space s p e e d space c a n n o t space b e space n e g a t i v e. T h u s space t h e space s p e e d space o f space t h e space s t r e m space i n space 3 space k m divided by h o u r

Answered by Vimala Ramamurthy | 3rd Jul, 2014, 09:35: AM

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