Question

In a stream runing 2 km/h a motorboat goes 6 km upstream and back again to the starting point in 33 minutes. find the speed of motorboat in still water

Answer 1

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$Let \: the \: Speed \: of \: boat \: in \: still \: water = x \: km/hr \\ \\ Speed \: of \: boat \: when \: goes \: upstream = (x - 2)kmhr \\ Speed \: of \: boat \: when \: goes \: downstream = (x + 2)km/hr \\ Given \: Distance = 6km \\ Given \: \: Time \: = 33minutes = \frac{33}{60} hr \\ \\ We \: know \: that ,\: Time = \frac{distance}{speed} \\ \\ Now ,\: Acc.to \: Statement : \\ \\ = > \frac{6}{(x + 2)} + \frac{6}{(x - 2)} = \frac{33}{60} \\ \\ = > \frac{6(x - 2) + 6( x + 2)}{x {}^{2} - 4 } = \frac{33}{60} \\ \\ = > \frac{6x - 12 + 6x + 12}{ {x}^{2} - 4 } = \frac{33}{60} \\ \\ = > \frac{12x}{ {x}^{2} - 4 } = \frac{33}{60} \\ \\ = > 60(12x) = 33( {x}^{2} - 4) \\ \\ = > 720x = 33 {x}^{2} - 132 \\ \\ = > 33 {x}^{2} - 132 - 720x = 0 \\ \\ = > 3(11 {x}^{2} - 240x - 44 = 0 \\ \\ = > 11 {x}^{2} - 242x + 2x - 44 = 0 \\ \\ = > 11x(x - 22) + 2(x - 22) = 0 \\ \\ = > (11x + 2)(x - 22) = 0 \\ \\ x = \frac{ - 2}{11} \: or \: x = 22 \\ \\Note : Speed \: can \: never \: be \: negative$

So, Speed of motorboat in still water is 22km /hr
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