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

12.32 km/h

Step-by-step 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,

`(54)/(V_b-V_r)+(54)/(V_b+V_r)=9\\\Rightarrow (54(V_b+V_r+V_b-V_r))/(V_b^2-V_r^2)=9\\\Rightarrow (54(2V_b))/(V_b^2-V_r^2)=9\\\Rightarrow (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=(12\pm √(144+16))/(2)=12.32\ or -0.32`

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