Final Answer:
The speed of the boat in still water is 28 miles per hour.
Step-by-step explanation:
Let the speed of the boat in still water be x mph and the speed of the current be y mph.
Traveling upstream:
Speed = x - y mph
Distance = 50 miles
Time = distance/speed = 50/(x - y) hours
Traveling downstream:
Speed = x + y mph
Distance = 62 miles
Time = distance/speed = 62/(x + y) hours
Given:
Speed of the current = y = 3 mph
We need to find:
Speed of the boat in still water = x
Setting up the equation:
Since the boat travels the same time upstream and downstream, we can set the two time equations equal to each other.
50/(x - y) = 62/(x + y)
Substituting the known value:
50/(x - 3) = 62/(x + 3)
Cross-multiplying:
50(x + 3) = 62(x - 3)
50x + 150 = 62x - 186
150 = 12x - 186
336 = 12x
x = 28 mph
Therefore, the speed of the boat in still water is 28 miles per hour.
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Complete Question
A boat travels 50 miles up the river in the same amount of time it takes to travel 62 miles down the same river. If the current is 3 miles per hour, what is the speed of the boat in still water?
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