Question : The speed of a boat upstream is 8 km/hr and the speed of a stream is 4 km/hr. The boat covers a distance of $x$ km in upstream and $x$ km in downstream. If the total time taken by the boat is 9 hours, then what is the value of $x$?
Option 1: 60 km
Option 2: 72 km
Option 3: 48 km
Option 4: 36 km
Correct Answer: 48 km
Solution :
Given: The speed of a boat upstream is 8 km/hr and the speed of a stream is 4 km/hr.
So, speed of the boat in the still water = 8 + 4 = 12 km/hr
Downstream speed = (The speed of the boat) + (The speed of the stream) = 12 + 4 = 16 km/hr
The total time taken by the boat is 9 hours.
So, $\frac{x}{8}+\frac{x}{16}=9$
⇒ $\frac{2x+x}{16}=9$
⇒ $3x=144$
⇒ $x=48$ km
Hence, the correct answer is 48 km.
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