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Question 604305: Hi! I think I got the correct answer to this word problem but am having trouble setting it up properly in a matrix (to get the right "output" answer). It is: when a crew rows with the current, it travels 16 miles in 2 hours. Against the current, the crew rows 8 miles in 2 hours. Let x=crew rowing rate in still water and y=rate of the current. I know rxt=d and x+y(t)=d and x-y(t)=d. I got x=6 and y=2. I have tried many different matrix "inputs" and just can't seem to get the right answer. I really wanted to figure it out on my own but am stuck. I know to line up the x's, y's, =k (constant). I need also to show the equation used.Thanks for any help!!!
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! a crew rows with the current, it travels 16 miles in 2 hours.
Against the current, the crew rows 8 miles in 2 hours.
Let x=crew rowing rate in still water and y=rate of the current.
We know
(x+y) = the effective speed downstream
and
(x-y) = effective speed upstream
:
Write a distance equation for each way
2(x+y) = 16
and
2(x-y) = 8
:
You can simplify both equations by dividing thru by 2
x + y = 8
x - y = 4
-----------adding eliminates y, find x
2x = 12
x = 6 mph in still water
then
6 + y = 8
y = 8 - 6
y = 2 is the rate of the current
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