A water boats whose speed in …

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.