A boat takes a total of 1.5 hours to cover 20km upstream and 15 km downstream. If the boat takes 4.8 hours to cover 120 km in still water, then find the time taken by a hat toflow for 32 km in the same stream
Speed of the boat in still water = 120 ÷ 4.8 = 25km/h Let the speed of the stream be 'x' km/h. ATQ. {20/ (25 - x)} + {15/(25 + x)} = (3/2) Or {20 X (25 + x) + 15 X (25 - x)} = (3/2) X (25 +x) X (25 - x) Or {(500 + 20x + 375 - 15x) X 2} = 3 X (625 -x²) Or, 1750 + 10x = 1875 - 3x² Or 3x² + 10x - 125 = 0 Or 3x² + 25x -15x - 125 = 0 Or x (3x + 25) - 5(3x + 25) = 0 Or (x - 5) (3x + 25) = 0 So, x = 5 or x = -(25/3) Since the speed of the stream cannot be negative therefore, speed of stream =5km/h so required time =D/s= 32/5 =6.4hours
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