Final answer:
The speed of the boat in still water can be solved by setting up an equation using the distances traveled up and down the river.
Step-by-step explanation:
Let's denote the speed of the boat in still water as x mph.
When the boat travels down the river, the effective speed will be the sum of the boat's speed and the speed of the current. So, the effective speed is (x + 1.8) mph.
When the boat travels up the river, the effective speed will be the difference between the boat's speed and the speed of the current. So, the effective speed is (x - 1.8) mph.
According to the given information, the time taken to travel 10 miles down the river is the same as the time taken to travel 8 miles up the river. Using the formula Distance = Speed x Time, we can set up the following equation:
10/(x + 1.8) = 8/(x - 1.8)
To solve for x, we can cross multiply and simplify the equation:
10(x - 1.8) = 8(x + 1.8)
10x - 18 = 8x + 14.4
2x = 32.4
x = 16.2
The speed of the boat in still water is 16.2 mph.
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