A sailor can row a boat …

Let the speed of the boat in still water be x km/hr.
Speed of the stream = 2 km/hr.
{tex}\therefore{/tex} speed downstream = (x + 2) km/hr,
speed upstream = (x - 2) km/hr.
Time taken by boat to go 8 km downstream = {tex}\frac{8}{x+2} {\ hr}{/tex} 

Time taken by boat to return 8 km upstream = {tex}\frac{8}{x-2} hr{/tex} 

Total time taken by boat = 1 hr and 40 minutes

According to question,
{tex}\therefore \quad \frac { 8 } { x + 2 } + \frac { 8 } { x - 2 } = \frac { 5 } { 3 }{/tex}
{tex}\Rightarrow \frac { 1 } { x + 2 } + \frac { 1 } { x - 2 } = \frac { 5 } { 24 } \Rightarrow \frac { ( x - 2 ) + ( x + 2 ) } { ( x + 2 ) ( x - 2 ) } = \frac { 5 } { 24 }{/tex}
{tex}\Rightarrow \frac { 2 x } { \left( x ^ { 2 } - 4 \right) } = \frac { 5 } { 24 } \Rightarrow{/tex} 5x² - 20 = 48x
{tex}\Rightarrow{/tex} 5x² - 48x - 20 = 0

{tex}\Rightarrow{/tex} 5x² - 50x + 2x - 20 = 0
{tex}\Rightarrow{/tex} 5x(x - 10) + 2(x - 10) = 0

{tex}\Rightarrow{/tex}(x - 10)(5x + 2) = 0
{tex}\Rightarrow{/tex} x - 10 = 0 or 5x + 2 = 0
{tex}\Rightarrow{/tex} x = 10 or x = {tex}\frac { - 2 } { 5 }{/tex}
{tex}\Rightarrow{/tex} x = 10 [{tex}\because{/tex} speed can't be negative]
Therefore, the speed of the boat is 10 km/hr.