Example 19 - A boat goes 30 km upstream and 44 km downstream - Examples

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Example 19 A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours, it can go 40 km upstream and 55 km down-stream. Determine the speed of the stream and that of the boat in still water. Let the speed of boat in still water be x km/hr & let the speed of current(stream) be y km/hr Speed downstream = Speed of boat in still water + Speed of stream Speed downstream = x + y Speed upstream = Speed of boat in still water Speed of stream Speed upstream = x y Given that A boat goes 30 km upstream and 44 km downstream in 10 hours Time taken to go 30 km upstream + Time taken to go 44 km downstream ( 30 )/( ) + ( 44 )/( ) = 10 30/( ) + 44/( + ) = 10 Similarly, A boat goes 40 km upstream and 55 km downstream in 13 hours Time taken to go 40 km upstream + Time taken to go 55 km downstream ( 40 )/( ) + ( 55 )/( ) = 13 40/( ) + 55/( + ) = 13 Our equations are 30 (1/( ))+44(1/( + ))=10 (1) 40 (1/( ))+55(1/( + ))=13 (2) Solving 30u + 44v = 10 (3) 40u + 55v = 13 (4) From (3) 30u + 44v = 10 30u = 10 44v u = (10 44 )/30 Putting value of u in (4) 40u + 55v = 13 40((10 44 )/30)+55 =13 4((10 44 )/3)+55 =13 Multiplying both sides by 3 3 4((10 44 )/3)+"3 " 55 ="3 " 13 4(10 44v) + 165 = 39 40 176v + 165v = 39 176v + 165v = 39 40 11v = -1 v = ( 1)/( 11) v = 1/11 Putting v = 1/11 in equation (3) 30u + 44v = 10 30u + 44(1/11) = 10 30u + 4 = 10 30u = 10 4 30u = 6 u = 6/30 u = 1/5 So, u = 1/5 & v = 1/11 So, u = 1/5 & v = 1/11 But we need to find x & y We know that So, our equations become x y = 5 (6) x + y = 11 (7) From (6) x y = 5 x = 5 + y Putting value of x in (7) x + y = 11 (5 + y) + y = 11 5 + 2y = 11 2y = 11 5 2y = 6 y =6/2 y = 3 Put y = 3 in (6) x y = 5 x 3 = 5 x = 5 + 3 x = 8 So, x = 8, y = 3 is the solution of the given equation Hence Speed of boat in still water = x = 8 km/hr Speed of stream = y = 3 km/hr

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.