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Speed of a boat in still …

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Speed of a boat in still water is 15km/h it goes 30km upstream and return back at the same point in 4 hours 30 minute . Find the speed of the stream

Posted by Jyoti Sahni 6 years, 4 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 4 months ago

Let the speed of the Stream be x km/hr.
{tex}\therefore {/tex} Speed of boat up stream = 15 - x
and speed of boat down stream = 15 + x
now according to the question

{tex}\frac { 30 } { 15 - x } + \frac { 30 } { 15 + x } = 4 \frac { 1 } { 2 }{/tex}

{tex}\frac { 30 ( 15 + x ) + 30 ( 15 - x ) } { 15 ^ { 2 } - x ^ { 2 } } = \frac { 9 } { 2 }{/tex}

{tex}900 \times 2 = 9 \left( 15 ^ { 2 } - x ^ { 2 } \right){/tex}

{tex}9 x ^ { 2 } = 2025 - 1800{/tex}

{tex}x ^ { 2 } = \frac { 225 } { 9 }{/tex}

{tex}x ^ { 2 } = 25 = \pm 5{/tex}

x = 5
Hence, the speed of the stream = 5 km/hr.

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