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Unformatted text preview: which we’re calling R. When traveling downstream, the river is helping Carl
along, so we add these two speeds:
rate traveling downstream = rate Carl propels the canoe + speed of the river
= 6 miles + R miles
So our downstream speed is (6 + R) miles . Substituting this into our ‘distance-rate-time’ equation
for the downstream part of the trip, we get:
5 miles = rate traveling downstream · time traveling downstream
5 miles = (6 + R) miles · time traveling downstream
3 In most textbooks, for example, they are handled by setting up one equation. Getting to that one equation,
however, essentially uses systems of equations. 8.7 Systems of Non-Linear Equations and Inequalities 539 When traveling upstream, Carl works against the current. Since the canoe manages to travel
upstream, the speed Carl can canoe in still water is greater than the river’s speed, so we subtract
the river’s speed from Carl’s canoing speed to get:
rate traveling upstream = rate Carl propels the can...
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