Question

A boat goes $64$ km upstream and $72$ km downstream in $14$ hrs. It goes $80$ km upstream and $96$ km downstream in $18$ hrs. Find the speed of the boat in still water and the speed of the stream.

Answer 1

Let the speed of boat in still water be $x$ and speed of stream be $y$

$\frac{64}{x-y}+\frac{72}{x+y}=14$

$\frac{80}{x-y}+\frac{96}{x+y}=18$

Let $x-y=a$ and $x+y=b$

$\Rightarrow \frac{64}{a}+\frac{72}{b}=14$ .....$\left(1\right)$

$\frac{80}{a}+\frac{96}{b}=18$ .....$\left(2\right)$

Multiply eqn$\left(1\right)$ by $4$ and eqn$\left(2\right)$ by $3$

$\Rightarrow \frac{256}{a}+\frac{288}{b}=56$

$\frac{240}{a}+\frac{288}{b}=54$

By subtracting the above equations, we get

$\frac{256-240}{a}=56-54=2$

$\Rightarrow \frac{16}{a}=2$

$\therefore 2a=16$ or $a=\frac{16}{2}=8$

Again, $\frac{240}{a}+\frac{288}{b}=54$

$\Rightarrow \frac{240}{8}+\frac{288}{b}=54$

$\Rightarrow \frac{288}{b}=54-30=24$

$\Rightarrow b=\frac{288}{24}=12$

$\therefore b=x+y=12$ and $a=x-y=8$

$a+b=x+y+x-y=12+8$

$\Rightarrow 2x=20$ or $x=\frac{20}{2}=10$ kmper hr.

$\Rightarrow x+y=12\Rightarrow y=12-x=12-10=2$ kmper hr.

$\therefore$ speed of the boat in still water be $10$ km per hr and speed of the stream be $2$ kmper hr