# A boat takes 4 hours to go 44 km downstream and it can go 20 km upstream at the same time. Find the speed of the stream and that of the boat in still water.

Given:
A boat takes 4 hours to go 44 km downstream and it can go 20 km upstream at the same time.
To do:
We have to find the speed of the stream and the speed of the boat in still water.
Solution:
Let the speed of the stream $=x\ km/hr$
Let the speed of the boat in still water $=y\ km/hr$
Upstream speed $=y−x\ km/hr$
Downstream speed $=y+x\ km/hr$
$time=\frac{speed}{distance}$
The boat goes $20\ km$ upstream in $4\ hours$.
Time taken $=\frac{20}{y−x}$
$4=​\frac{20}{y−x}$
$4(y-x)=20$
$y-x=5$.....(i)
The boat goes $44\ km$ downstream in $4\ hours$.
Time taken $=\frac{44}{y+x}$
$4=​\frac{44}{y+x}$
$4(y+x)=44$
$y+x=11$.....(ii)
Adding equations (i) and (ii), we get,

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

$2y=16$

$y=\frac{16}{2}$

$y=8\ km/hr$

This implies,

$8-x=5$

$x=8-5$

$x=3\ km/hr$

Therefore,

Speed of the stream is 3 km/hr and the speed of the boat in still water is 8 km/hr.

Updated on: 10-Oct-2022

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