Question
✓
Answer
Let the speed of the boat in still water be $x km / hr$ and the speed of water current be $y km / hr$
$\therefore$ speed of boat in downstream $=(x+y) km / hr$. and that in upstream $=(x-y) km / hr$.
Now distance $=$ speed $\times$ time
$\therefore \text { time }=\frac{\text { distance }}{\text { speed }}$
Time taken by the boat to travel $16 km$ upstream $=\frac{16}{x-y}$ hours and it takes $\frac{24}{x+y}$ hours to travel $24 km$ downstream.
from first condition -
$\frac{16}{x-y}+\frac{24}{x+y}=6 \ldots (I)$
from $2^{\text {nd }}$ condition
$\frac{36}{x-y}+\frac{48}{x+y}=13 \ldots (II)$
By replacing $\frac{1}{x-y}$ by $m$ and $\frac{1}{x+y}$ by $n$ we get
$\begin{aligned}
& 16 m+24 n=6 \ldots \text { (III) } \\
& 36 m+48 n=13 \ldots \text { (IV) }
\end{aligned}$
Solving equations (III) and (IV) $m=\frac{1}{4}, n=\frac{1}{12}$
Repalcing $m, n$ by their original values we get
$x-y=4 \ldots \text { (V) } x+y=12 \ldots \text { (VI) }$
Solving equations (V), (VI) we get $x=8, y=4$
$\therefore$ speed of the boat in still water is $8 km / hr$. and speed of water current is $4 km / hr$.
$\therefore$ speed of boat in downstream $=(x+y) km / hr$. and that in upstream $=(x-y) km / hr$.
Now distance $=$ speed $\times$ time
$\therefore \text { time }=\frac{\text { distance }}{\text { speed }}$
Time taken by the boat to travel $16 km$ upstream $=\frac{16}{x-y}$ hours and it takes $\frac{24}{x+y}$ hours to travel $24 km$ downstream.
from first condition -
$\frac{16}{x-y}+\frac{24}{x+y}=6 \ldots (I)$
from $2^{\text {nd }}$ condition
$\frac{36}{x-y}+\frac{48}{x+y}=13 \ldots (II)$
By replacing $\frac{1}{x-y}$ by $m$ and $\frac{1}{x+y}$ by $n$ we get
$\begin{aligned}
& 16 m+24 n=6 \ldots \text { (III) } \\
& 36 m+48 n=13 \ldots \text { (IV) }
\end{aligned}$
Solving equations (III) and (IV) $m=\frac{1}{4}, n=\frac{1}{12}$
Repalcing $m, n$ by their original values we get
$x-y=4 \ldots \text { (V) } x+y=12 \ldots \text { (VI) }$
Solving equations (V), (VI) we get $x=8, y=4$
$\therefore$ speed of the boat in still water is $8 km / hr$. and speed of water current is $4 km / hr$.
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