Question: A boat goes 12 km downstream and comes back to the starting point in 3 h. If the speed of current is 3 km/h, then the speed (in km/h) of the boat in still water is
Options:
A) 12
B) 9
C) 8
D) 6
Show Answer
Answer:
Correct Answer: B
Solution:
- If the speed of boat in still water be $ xkm/h. $
Then, speed in downstream $ =(x+3)km/h $
Speed in upstream $ =(x-3)km/h $
According to the question,
$ \frac{12}{x+3}+\frac{12}{x-3}=3 $
$ \Rightarrow $ $ \frac{12x-36-12x+36}{x^{2}-9}=3 $
$ \Rightarrow $ $ 3x^{2}-27=24x $
$ \Rightarrow $ $ x^{2}-8x-9=0 $
$ \Rightarrow $ $ (x-9)(x+1)=0 $
$ \Rightarrow $ $ x\ne 1 $
$ \therefore $ $ x=9km/h $