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a boat travels 50 upstream against the current in the same amount of time it takes to travel downstream with the current. if the current is , what is the speed of the boat in still water?

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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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User Daniel Jihoon Oh
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