Question

The speed of the current in a river 6 mph. A very operator who works top part of the river is looking to buy a new boat for his business. Every day, his route takes him 22.5 miles each way against the current back back to the dock, and he needs to make his trip any tour of nine hours. He has a bow in mind, but he can only test it on a leak where there is no current. How fast must the boat go on the lake in order for it to serve the ferry operators needs?

Answer 1

Answer:

9 mph

Step-by-step explanation:

Speed of current = 6 mph

Distance to travel one way = 22.5 miles

Let speed of the ferry be $x$ mph

Total time taken for round trip is 9 hours

One way the ferry will be going with the current and in the other way the ferry will be going against the current so

$\dfrac{22.5}{x+6}+\dfrac{22.5}{x-6}=9\\\Rightarrow \dfrac{x-6+x+6}{x^2-36}=\dfrac{9}{22.5}\\\Rightarrow \dfrac{2x}{x^2-36}=0.4\\\Rightarrow \dfrac{2x}{x^2-36}-0.4=0\\\Rightarrow 2x-0.4x^2+14.4=0\\\Rightarrow 0.4x^2-2x-14.4=0\\\Rightarrow 4x^2-20x-144=0\\\Rightarrow x=\dfrac{-\left(-20\right)\pm \sqrt{\left(-20\right)^2-4\times 4\left(-144\right)}}{2\times 4}\\\Rightarrow x=9,-4$

So, the speed of the boat in still water needs to be 9 mph both ways.