Two neighboring towns, Serenityville and Concordburg, are positioned 84 miles apart along the serene Tranquil River. A nimble speedboat travels between these towns, completing the round trip smoothly. The constant current of the river flows at 12 miles per hour. The speedboat manages to finish the entire round trip in over 24 hours, without any breaks in the journey. What is the highest speed of the boat that could achieve in waters (in miles/hour)?

Using the total time formula for the 84-mile round trip where b is the boat's speed in still water, we establish 84/(b-12) + 84/(b+12) > 24. Factoring out 84 gives 84 [ 1/(b-12) + 1/(b+12) ] > 24, which simplifies to 84 [ 2b / (b^2 - 144) ] > 24 and then to 7b > b^2 - 144. Rearranging terms provides the quadratic inequality b^2 - 7b - 144 < 0, which factors to (b-16)(b+9) < 0, meaning b must be between -9 and 16. Since the boat's speed must exceed the 12 mph current to move upstream, the maximum integer speed satisfying the condition is 16.

• Thanks
• Wrong explanation