Question
A man rows 45 km downstream and 27 km upstream in a
total of 6 hours. If the speed of the stream is 3 km/h, find the speed of the boat in still water.Solution
Let boat speed in still water = b km/h Downstream speed = b + 3, upstream speed = b − 3 Equation: [45/(b+3)] + [27/(b−3)] = 6 45(b−3) + 27(b+3) = 6(b²− 9) 45b − 135 + 27b + 81 = 6b²− 54 72b − 54 = 6b²− 54 6b²− 72b = 0 ⇒ 6b(b−12) = 0 ⇒ b = 12.
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