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According to the question,A motorboat whose speed in still water is 18 km/h, takes 1 hour more to go 24 km upstream than to return downstream to the same spot.
Let the speed of stream be x km/h
Then the speed of boat upstream = (18 - x) km/h
Speed of boat downstream = (18 + x) km/h
According to the question,
{tex}\frac { 24 } { 18 - x } - \frac { 24 } { 18 + x } = 1{/tex}
{tex}\frac { 24 ( 18 + x ) - 24 ( 18 - x ) } { (18 - x )(18+x)} = 1{/tex}
{tex}\frac { 24 ( 18 + x ) - 24 ( 18 - x ) } { 18 ^ { 2 } - x ^ { 2 } } = 1{/tex}
{tex}432 + 24 x - 432 + 24 x = 324 - x ^ { 2 }{/tex}
{tex}48 x = 324 - x ^ { 2 }{/tex}
{tex}x ^ { 2 } + 48 x - 324 = 0{/tex}
{tex}x ( x + 54 ) - 6 ( x + 54 ) = 0{/tex}
{tex}( x + 54 ) ( x - 6 ) = 0{/tex}
x + 54 = 0, x - 6 = 0
x = - 54, x = 6
Since speed cannot be negative
The speed of steam x = 6 km/h.
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Nishant Verma 7 years, 9 months ago
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