Answer :
Answer:
12.32 km/h
Explanation:
[tex]V_r[/tex]=Velocity of river = 2 km/h
[tex]V_b[/tex]=Velocity of boat
[tex]V_b-V_r[/tex] = Speed of boat going against river
[tex]V_b+V_r[/tex] = Speed of boat going along river
Distance to travel = 54 km
Total time taken = 9 hours
So,
[tex]\frac{54}{V_b-V_r}+\frac{54}{V_b+V_r}=9\\\Rightarrow \frac{54(V_b+V_r+V_b-V_r)}{V_b^2-V_r^2}=9\\\Rightarrow \frac{54(2V_b)}{V_b^2-V_r^2}=9\\\Rightarrow \frac{54(2V_b)}{9}=V_b^2-V_r^2\\\Rightarrow 12V_b=V_b^2-V_r^2\\\Rightarrow V_b^2-V_r^2-12V_b=0\\\Rightarrow V_b^2-12V_b-4=0[/tex]
Solving this quadratic equation we get,
[tex]V_b=\frac{12\pm \sqrt{144+16}}{2}=12.32\ or -0.32[/tex]
So, velocity of boat in still water is 12.32 km/h