A boat goes 24 km upstream and 28 km downstream in 6 hours. It goes 30 km upstream and 21 km downstream in 6 1 2 hours. Find the speed of the boat in still water and speed of the stream.

Let the speed of the boat in still water be x km / hr and the speed of the stream be y km / hr . Speed upstream = x - y km / hr Sped down stream = x + y km / hr Time taken to cover 28 km downstream = 28 x + y hours Time taken to cover 24 km upstream = 24 x - y hours Total time of journey is 6 hours 24 x - y + 28 x + y = 6 … ( i ) Time taken to cover 30 km upstream = 30 ( x - y ) hours Time taken to cover 21 km downstream = 21 x + y hours In this case total time of journey is given to 6 1 2 hours or 13 2 hours 30 x - y + 30 x + y = 13 2 … ( i i ) By 1 x - y = u and 1 x + y = v in ( i ) and ( i i ) equation we get, 24 u + 28 v - 6 = 0 … ( i i i ) 30 u + 21 v - 13 2 = 0 … ( i v ) By cross multiplication, u ( 28 × - 13 2 - 21 × - 6 ) = ( - v ) ( 24 × - 13 2 - 30 × - 6 ) = 1 ( 24 × 21 - 30 × 28 ) u - 56 = - v 24 = 1 - 336 u = - 56 - 336 = 1 6 and v = - 24 - 336 = 1 14 u = 1 6 and v = 1 14 Now, u = 1 x - y = 1 6 ⇒ 6 = x - y … v v = 1 14 = 1 x + y ⇒ x + y = 14 … ( v i ) Adding equations v and v i we get, x - y + x + y = 6 + 14 ⇒ 2 x = 20 ⇒ x = 20 2 = 10 By substituting x = 10 in equation v i we get, 10 + y = 14 ⇒ y = 4 Hence, the speed of the stream is 4 km / hr . The speed of boat is 10 km / hr .