Asked by heyo ❄

8. 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 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? *
Answered by mathhelper
Speed of boat he needs --- x mph
Speed with the current = x + 6 mph
speed against the current = x - 6 mph

22.5/(x+6) + 22.5/(x-6) ≤ 9
let's use the equality...
multiply each term by (x-6)(x+6)
22.5(x-6) + 22.5(x+6) = 9(x-6)(x+6)
22.5x - 135 + 22.5x + 135 = 9x^2 - 324
9x^2 - 45x - 324 = 0
x^2 - 5x + 36 = 0
(x - 9)(x + 4) = 0
x = 9 or x = -4, but we obviously reject the x = -4

His new boat must be able to go at least 9 mph, (slow boat?)

Answered by heyo ❄
tysm
Answered by random
Thank you Mathhelper!
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