Question

A boat travels 26 miles up a river in the same amount of time it takes to travel 38 miles down the same river. If the current is 3 mph, what is the speed of the boat in till water?

Answer 1

Let the speed of the boat in still water = X

The current is 3 mph, so the speed of the boat going upstream would be x-3

Speed of the boat going down stream would be x +3

The trip upstream is 26 / x-3

The trip downstream is 38 / x+3

Set them to equal and solve for x:

26/x-3 = 38/x+3

Multiply both sides by (x+3)(x-3):

38(x-3) = 26(x+3)

Simplify:

38x - 114 = 26x+78

Subtract 26x from each side:

12x -114 = 78

Add 114 to each side:

12x = 192

Divide both sides by 12:

x = 192 / 12

x = 16

The speed is 16 miles per hour.