The speed of a boat in …

Given, speed of boat in still water = 8 Km/hr. Let the speed of the stream be x km/hr. Then,
Speed of boat in downstream = (8 + x) km/hr
Speed of boat in upstream  = (8 - x) km/hr
We know that time taken to cover 'd' km with speed 's' km/hr is  {tex} \frac ds{/tex}

So,Time taken by the boat to go 15 km upstream {tex} = \frac{{15}}{{8 - x}}{/tex} hours.
&,   Time taken by the boat to 22 km downstream {tex} = \frac{{22}}{{8 + x}}{/tex} hours.
It is given that the total time taken by boat to go 15 km upstream & 22 km downstream is 5 hours.
{tex}\therefore \frac{{15}}{{8 - x}} + \frac{{22}}{{8 + x}} = 5{/tex}
{tex} \Rightarrow \frac{{15(8 + x) + 22(8 - x)}}{{(8 - x)(8 + x)}} = 5{/tex}
{tex} \Rightarrow \frac{{120 + 15x + 176 - 22x}}{{{8^2} - {x^2}}} = 5{/tex}
{tex} \Rightarrow \frac{{ - 7x + 296}}{{64 - {x^2}}} = 5{/tex}
{tex}\Rightarrow{/tex} -7x + 296 = 5(64 - x²)
{tex}\Rightarrow{/tex} -7x + 296 = 320 - 5x²
{tex}\Rightarrow{/tex} 5x² - 7x + 296 - 320 = 0
{tex}\Rightarrow{/tex} 5x² - 7x - 24 = 0
{tex}\Rightarrow{/tex} 5x² - 15x + 8x - 24 = 0
{tex}\Rightarrow{/tex} 5x(x - 3) + 8(x - 3) = 0
{tex}\Rightarrow{/tex} (5x + 8)(x- 3) = 0
{tex}\Rightarrow{/tex} x - 3 = 0 [{tex}\because{/tex} Speed can not be negative {tex}\therefore{/tex} 5x + 8 {tex}\ne{/tex} 0]
{tex}\Rightarrow{/tex} x = 3
Hence, the speed of the stream is 3 km/hr.