the speed of the current in a river is 6 mph a ferry operator who works that part of the river is looking to buy a new boat for his business everyday his route takes him 22.5 miles against the current and back to his deck and he needs this trip in a total of 9 hours he has a boat in mind but he can only test it on a lake where there in no current how fast must the boat go on the lake in order for it to serve the ferry operators needs

Question

can someone please explain?

Answer 1

(22.5/r-6)+(22.5/r+6)=9
Multiply the equation by r^2-36.
Resulting equation: 9r^2-45r-324=0
Simplify: r^2-5r-36=0
Factor: (r-9)(r+4)
Answer: rate of ferry= 9mph