Question : A boat travels 32 km downstream in 4 hours and 24 km upstream in 6 hours. What is the speed (in km/hr) of a boat in still water?
Option 1: 2
Option 2: 4
Option 3: 6
Option 4: 8
Correct Answer: 6
Solution :
Let $x$ km/hr be the speed of the boat in still water and $y$ km/hr be the speed of the current.
The speed of the boat downstream = $(x+y)$ km/hr
The speed of the boat in upstream = $(x–y)$ km/hr
The distance travelled upstream = $24$ km
A boat travels 32 km downstream in 4 hours and 24 km upstream in 6 hours.
$\text{Speed}=\frac{\text{Distance}}{{\text{Time}}}$
$6(x-y)=24⇒x-y=4$
$4(x+y)=32⇒x+y=8$
Solving the above equations, we get,
$2x=12⇒x=6$ km/hr
Hence, the correct answer is 6.
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