Question : A boat goes 20 km upstream and 44 km downstream in 8 hours. In 5 hours, it goes 15 km upstream and 22 km downstream. Determine the speed of the boat in still water.
Option 1: 6 km/h
Option 2: 10 km/h
Option 3: 8 km/h
Option 4: 7 km/h
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Correct Answer: 8 km/h
Solution :
Let the speed of the boat in still water be $x$ km/h and
The speed of stream = $y$ km/h
Speed of boat at downstream = $(x+y)$ km/h
Speed of boat at upstream = $(x−y)$ km/h
Time taken to cover 20 km upstream = $\frac{20}{x-y}$
Time taken to cover 44 km downstream = $\frac{44}{x+y}$
According to the question,
$\frac{20}{x-y}+ \frac{44}{x+y} = 8$ .......(1)
Also,
$\frac{15}{x-y}+ \frac{22}{x+y} = 5$ .......(2)
Now let $\frac{1}{x-y} = u$ and $\frac{1}{x+y} = v$
$\therefore$ equation (1) and (2) becomes,
$20u + 44v = 8$
$15u +22v = 5$
Solving these equations, we get
$u = \frac{1}{5}$
$v = \frac{1}{11}$
⇒ $x-y = 5$ and $x+y = 11$
$\therefore$ $x = 8$ and $y = 3$
The speed of the boat in still water = $x$ = 8 km/h
Hence, the correct answer is 8 km/h.
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