SOLUTION: A boat can travel 14 miles upstream in the same amount of time it takes to travel 21 miles downstream. If the current is 2 miles per hour, what is the speed of the boat in still wa

Question 204259: A boat can travel 14 miles upstream in the same amount of time it takes to travel 21 miles downstream. If the current is 2 miles per hour, what is the speed of the boat in still water?
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Use the distance formula:
where: d = distance trveled, r = rate(speed), and t = time of travel.
For the trip upstream (against the current of 2mph), d = 14mi. and r = speed of the boat, so you can write:
The speed of the current is subtracted from the speed of the boat going upstream.
For the trip downstream (with the current of 2mph), d = 21mi, and r = the speed of the boat, so you can write:
The time, t, is the same in both cases, so we solve both equations for t and set them equal to each other.
Upstream trip:

Downstream trip:
Set these equal to each other.
Solve for r, the speed of the boat in still water. Cross multiply.
Simplify.
Subtract 14r from both sides.
Add 42 to both sides.
Finally, divide both sides by 7.

The speed of the boat in still water is 10mph.

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