SOLUTION: please explain the step for this I have no idea. 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 hi

Algebra ->  Rational-functions -> SOLUTION: please explain the step for this I have no idea. 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 hi      Log On


   

Question 707663: please explain the step for this I have no idea.
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
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
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
----
Solve for boat speed in still water.
---
Against current DATA:
distance = 22.5 miles ; rate = b-6 mph ; time = d/r = 22.5/(b-6) hrs.
-----
With current DATA:
distance = 22.5 miles ; rate = b+6 mph ; time = d/r = 22.5/(b+6) hrs
----
Equation:
time + time = 9 hrs
22.5/(b-6) + 22.5/(b+6) = 9 hrs
------
22.5(b+6) + 22.5(b-6) = 9(b^2-36)
45b = 9(b^2-36)
5b = b^2-36
b^2-5b-36 = 0
Factor:
b^2-9b+4b-36 = 0
b(b-9)+4(b-9) = 0
(b-9)(b+4) = 0
----
Positive solution:
b = 9 mph (required speed of the boat in still water)
=================
Cheers,
Stan H.
====================