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
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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) (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
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Solve for boat speed in still water.
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Against current DATA:
distance = 22.5 miles ; rate = b-6 mph ; time = d/r = 22.5/(b-6) hrs.
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With current DATA:
distance = 22.5 miles ; rate = b+6 mph ; time = d/r = 22.5/(b+6) hrs
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Equation:
time + time = 9 hrs
22.5/(b-6) + 22.5/(b+6) = 9 hrs
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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
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Positive solution:
b = 9 mph (required speed of the boat in still water)
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Cheers,
Stan H.
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