Question

The boat goes $24$ km upstream and $28$ km downstream in $6$ hrs. It goes $30$ km upstream and $21$ km downstream in $6\frac{1}{2}$ hrs. Find the speed of the boat in still water and also speed of the stream.

Answer 1

Let the boat speed be $x$ and

the stream speed be $y$

Given that the taken for the boat to go $24km$ upstream and $28km$ downstream is $6hrs$

we know that $time=\frac{distance}{speed}$

Therefore, time taken for the to go upstream is $\frac{24}{x-y}$ and

time taken for the to go downstream is $\frac{28}{x+y}$

Hence, $\frac{24}{x-y}+\frac{28}{x+y}=6$ ---------(1)

Given that the taken for the boat to go $30km$ upstream and $21km$ downstream is $6.5hrs$

Therefore, time taken for the to go upstream is $\frac{30}{x-y}$ and

time taken for the to go downstream is $\frac{21}{x+y}$

Hence, $\frac{30}{x-y}+\frac{21}{x+y}=6.5$ ---------(2)

Let $\frac{1}{x-y}=p$ and $\frac{1}{x+y}=q$

Therefore, (1) and (2) becomes

$24p+28q=6⟹12p+14q=3$ -----(3)

and $30p+21q=6.5$ -----(4)

eqn (3)*3- eqn (4)*2 we get

$36p-60p=9-13$

$⟹p=\frac{4}{24}=\frac{1}{6}$ -----(5)

substituting (5) in (3) we get

$2+14q=3$

$⟹q=\frac{1}{14}$ -----(6)

Therefore, $x-y=6$ and $x+y=14$

solving the equations we get

$x=10$ and $y=4$

Therefore, the boat speed is $10kmph$ and

the stream speed is $4kmph$