SOLUTION: A boat moves 6 kilometers upstream in the same amount of time it moves 16 kilometers downstream. If the rate of the current is 8 kilometers per hour, find the rate of the boat in s

Algebra ->  Test -> SOLUTION: A boat moves 6 kilometers upstream in the same amount of time it moves 16 kilometers downstream. If the rate of the current is 8 kilometers per hour, find the rate of the boat in s      Log On


   

Question 1137613: A boat moves 6 kilometers upstream in the same amount of time it moves 16 kilometers downstream. If the rate of the current is 8 kilometers per hour, find the rate of the boat in still water.
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


Here are two different ways to set up the problem that lead to different forms of the same proportion that leads to the answer to the problem.

Let b be the boat's speed; then b+8 is the downstream speed and b-8 is the upstream speed.

(1) Time = distance / rate. Write and solve the proportion that says the times are the same:

16%2F%28b%2B8%29+=+6%2F%28b-8%29

(2) Write and solve the proportion that says the ratio of speeds is the same as the ratio of distances, because the times are the same:

%28b%2B8%29%2F%28b-8%29+=+16%2F6

It should be clear that the two proportions are equivalent and so will lead to the same answer.

Try both methods for setting up the problem; then if you encounter more problems like this, use the method you find is easier for you.