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Question 82668: This problem is not from a textbook:
I understand that I need to create two equations but I am not sure how to formulate them. I am not sure how to position the variables in the "rate x time = distance" formula...
In a canoe race, a team paddles downstream 560 meters in 70 seconds. The same team makes the trip back upstream to the starting point in 80 seconds. First, write a system of two equations in two variables that models the problem. (Let r = the rate of the canoe team in still water and c = the rate of the current.
Second, find the team's rate in still water and the rate of the current
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! In a canoe race, a team paddles downstream 560 meters in 70 seconds. The same team makes the trip back upstream to the starting point in 80 seconds. First, write a system of two equations in two variables that models the problem. (Let r = the rate of the canoe team in still water and c = the rate of the current.
Second, find the team's rate in still water and the rate of the current
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Downstream DATA:
distance = 560 m ; time = 70 sec ; rate = 560/70 = 8 m/sec
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Upstream DATA:
distance = 560 m ; time = 80 sec; rate = 560/80 = 7 m/sec
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Let rate in still water be s; Let rate of current be c:
EQUATIONS:
s+c = 8 m/sec
s-c = 7 m/sec
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Add the two equation to solve for "s":
2s = 15
s=7.5 m/sec (this is the rate of the boat in still water)
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Substitute to solve for "c":
7.5-c=7
c=0.5 m/sec (this is the rate of the current)
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Cheers,
Stan H.
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