A sailor goes 8km downstream in 40 minutes and returns in 1 hour. Find the speed of the sailor in still water and the speed of current.

Asked by Anjana S | 14th Jul, 2014, 05:20: 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 a i l o r space a n d space y space b e space t h e space s p e e d space o f space w a t e r space c u r r e n t. T h e n space s p e e d space o f space u p s t r e a m space i s space x minus y space 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 x plus y G i v e n space t h a t space t h e space s a i l o r space g o e s space 8 k m space d o w n s t r e a m space i n space 40 space m i n u t e s space a n d space r e t u r n s space i n space 1 space h o u r. rightwards double arrow fraction numerator 8 over denominator x plus y end fraction equals 40 over 60... left parenthesis 1 right parenthesis fraction numerator 8 over denominator x minus y end fraction equals 1... left parenthesis 2 right parenthesis 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 2 x plus 2 y equals 24.. left parenthesis 3 right parenthesis x minus y equals 8... left parenthesis 4 right parenthesis M u l t i p l y i n g space t h e space e q u a t i o n space left parenthesis 4 right parenthesis space b y space 2 space a n d space a d d i n g space t h e space r e s u l t i n g space e q u a t i o n space w i t h space e q u a t i o n space left parenthesis 3 right parenthesis comma space w e space h a v e comma 4 x equals 40 rightwards double arrow x equals 10 S u b s t i t u t i n g space t h e space v a l u e space o f space x space i n space e q u a t i o n space left parenthesis 4 right parenthesis comma space w e space h a v e comma y equals 2 T h u s comma space t h e space s p e e d space o f space t h e space s a i l o r space i s space 10 k m divided by h r space a n d space t h e space s p e e d space o f space t h e space w a t e r space c u r r e n t space i s space 2 space k m divided by h r. space

Answered by Vimala Ramamurthy | 15th Jul, 2014, 11:56: AM