Question

the speed of a boat in still water is 11km/hr. it can go 12km upstream and return downstream to the original point in 2hrs 45min . find the speed of the stream

Answer 1

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Solution:-

Speed Of Still Water = 11 km/hr.

Let the Speed of Stream be x km/hr.

Distance = 12 km.

For Upstream,

$time = \frac{12}{11 - x}$

& For Downstream,

$time = \frac{12}{x + 11}$

A.T.Q.

$= > \frac{12}{x + 11} + \frac{12}{11 - x} = 2 hour \: 45min \\ \\ = > \frac{12(11 - x) + 12(11 + x)}{(11 - x)(11 + x)} = 2 \times \frac{45}{60} \\ \\ = > 12\frac{(11 - x + 11 + x)}{121 - {x}^{2} } = \frac{11}{4} \\ \\ = > \frac{12 \times 22}{121 - {x}^{2} } = \frac{11}{4} \\ \\ = > 264 \times 4 = 1331 - 11 {x}^{2} \\ \\ = > 11 {x}^{2} = 1331 - 1056 \\ \\ = > 11 {x}^{2} = 275 \\ \\ = > {x}^{2} = \frac{275}{11} \\ \\ = > {x}^{2} = 25 \\ \\ = > x = 5 \: \: \: \: \: and \: - 5(neglect).$

Hence,

Speed of Stream = 5 km/hr.