Goal: Solve a word problem to find the right input value to a quadratic function

Question

Goal: Solve a word problem to find the right input value to a quadratic function

1. A river boat travels up and down the Mississippi River carrying supplies back and forth between a production facility and a barge construction site that are 10 kilometers apart. The river has a current of 1 kilometer per hour. Round trip time for the boat (in hours) can be modeled as t=10x1+10x+1t=10x1+10x+1 where xx is the speed of the boat in kilometers per hour. At what speed xx should the boat travel to make a round trip in 4 hours? (Round your answer to 2 decimal places.)

Explanation / Answer

10/(x-1) + 10/ ( x+1) = 4

(10x +10 + 10x - 10)/ (x^2-1) = 4

20x = 4x^2- 4

4x^2-20x-4= 0

x^2-5x-1=0

x5.19258240,0.19258240

therefore, the speed of boat in still water is 5.19km/hr

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