Question

The boat goes $30$ km upstream and $44$ km downstream in $10$ hrs. In $13$ hours, it can go $40$ km upstream and $55$ km downstream. Determine the product of speed of stream and that of the boat in still water.

Answer 1

Let the speed of the boat in still water $=xkmph$ and that of the stream be $ykmph$.

Speed upstream $=(x-y)kmph$

Speed downstream $=(x+y)kmph$

Time taken to cover $30km$ upstream $=30/(x-y)hrs$

Time taken to cover $44km$ downstream $=44/(x+y)hrs$

So,

$30/(x-y)+44/(x+y)=\mathrm{10.....}\left(1\right)$

Similarly, we get

$40/(x-y)+55/(x+y)=\mathrm{13.....}\left(ii\right)$

Putting $1/(x-y)=u$ and $1/(x+y)=v$, we get

$30u+44v=\mathrm{10....}\left(iii\right)$

$40u+55v=\mathrm{13......}\left(iv\right)$

Solving $\left(iii\right)$ and $\left(iv\right)$, we get $u=1/5$ and $v=1/11$

Equating values of $u$ and $v$ with $1/(x-y)$ and $1/(x+y)$ respectively, we get

$1/(x-y)=1/5$ and $1/(x+y)=1/11$

$x-y=5$ and $x+y=11$

solving these equations, we get, $x=8kmph$ and $y=3kmph$

So, product of speed of stream and speed of boat in still water $=8\times 3=24$