A boat travels 54 miles downstream in 3 hours and 72 miles upstream in 4 hours. What is the speed of the boat in still water?
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Let's denote the speed of the boat in still water as "b" (in miles per hour), and the speed of the current as "c" (in miles per hour).
When the boat travels downstream, its effective speed is increased by the speed of the current. Therefore, the speed downstream is: b + c.
When the boat travels upstream, its effective speed is decreased by the speed of the current. Therefore, the speed upstream is: b - c.
Given that the boat travels 54 miles downstream in 3 hours, we can write the equation:
54 = (b + c) * 3
Simplifying this equation gives us:
18 = b + c ---> Equation (1)
Also, given that the boat travels 72 miles upstream in 4 hours, we can write the equation:
72 = (b - c) * 4
Simplifying this equation gives us:
18 = b - c ---> Equation (2)
Now, we have a system of equations to solve. We can solve it using the method of elimination.
Adding Equation (1) and Equation (2) eliminates the term "c" and gives us:
2b = 36
Dividing both sides by 2 gives us the value of "b":
b = 18
Therefore, the speed of the boat in still water is 18 miles per hour.
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