Question

A river flows at a rate of 2 km divided by h. A patrol boat travels 54 km upriver and returns in a total time of 9 hr. What is the speed of the boat in still​ water?

Answer 1

Answer:

12.32 km/h

Explanation:

$V_r$=Velocity of river = 2 km/h

$V_b$=Velocity of boat

$V_b-V_r$ = Speed of boat going against river

$V_b+V_r$ = Speed of boat going along river

Distance to travel = 54 km

Total time taken = 9 hours

So,

$\frac{54}{V_b-V_r}+\frac{54}{V_b+V_r}=9\\\Rightarrow \frac{54(V_b+V_r+V_b-V_r)}{V_b^2-V_r^2}=9\\\Rightarrow \frac{54(2V_b)}{V_b^2-V_r^2}=9\\\Rightarrow \frac{54(2V_b)}{9}=V_b^2-V_r^2\\\Rightarrow 12V_b=V_b^2-V_r^2\\\Rightarrow V_b^2-V_r^2-12V_b=0\\\Rightarrow V_b^2-12V_b-4=0$

Solving this quadratic equation we get,

$V_b=\frac{12\pm \sqrt{144+16}}{2}=12.32\ or -0.32$

So, velocity of boat in still water is 12.32 km/h