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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. Every day, his route takes him 22.5 miles each way against the current
and back to his dock, and he needs to make 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 is no current. How fast must the boat go on the lake in order for it to
serve the ferry operator's needs?

Sagot :

mhanifa

Answer:

  • 9 mph

Step-by-step explanation:

Let he speed of the boat on the lake is x.

Considering the speed of the current it will take him:

  • 22.5/(x + 6) + 22.5/(x - 6) = 9
  • 2.5 / (x  + 6) + 2.5 / (x - 6) = 1
  • 2.5(x - 6 + x + 6) = (x + 6)(x - 6)
  • 2.5*2x = x² - 36
  • x² - 5x - 36 = 0
  • x = (5 ± √(5² + 4*36))/2 = (5 ± 13) / 2
  • x = (5 + 13)/2 = 9 mph (negative root is discarded as the speed should be positive)
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