SOLUTION: On a certain river, a paddleboat travels 4 miles upstream (against the current) in the same amount of time it travels 8 miles downstream (with the current). if the current of the

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Question 1040586: On a certain river, a paddleboat travels 4 miles upstream (against the current) in the same amount of time it travels 8 miles downstream (with the current). if the current of the river is 1 mile per hour, determine the speed of the boat in still water.
Answer by ikleyn(52855) About Me  (Show Source):
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On a certain river, a paddleboat travels 4 miles upstream (against the current) in the same amount of time
it travels 8 miles downstream (with the current). if the current of the river is 1 mile per hour,
determine the speed of the boat in still water.
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Your equation is

4%2F%28u-1%29 = 8%2F%28u%2B1%29.

Here "u" is an unknown speed of the boat in still water, in mph.
Left side is the time spent for the travel upstream.
Right side is the time spent for the travel downstream.

Multiply both sides by (u+1)*(u-1). You will get

4*(u+1) = 8*(u-1),   or

4u + 4 = 8u - 8,   or

4 + 8 = 8u - 4u,   or

4u = 12,

u = 12%2F4 = 3.

Answer.  The speed of the boat in still water is 3 mph.

For many other Travel and Distance problem of the same type see the lessons
    - Wind and Current problems
    - More problems on upstream and downstream round trips
    - Wind and Current problems solvable by quadratic equations
    - Selected problems from the archive on the boat floating Upstream and Downstream
    - Selected problems from the archive on a plane flying with and against the wind
in this site.