SOLUTION: A boat can go 33 mph in still water. It takes as long to go 300 miles upstream as it does to go downstream 360 miles. How fast is the current?

Question 173619This question is from textbook Introductory Algebra
: A boat can go 33 mph in still water. It takes as long to go 300 miles upstream as it does to go downstream 360 miles. How fast is the current? This question is from textbook Introductory Algebra

Answer by gonzo(654) (Show Source): You can put this solution on YOUR website!
rate of the boat = 33 mph.
rate of the water = c miles per hour.
t = amount of time it takes to go upstream = amount of time it takes to go downstream.
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rate * time = distance
going upstream (against the current), the equation is:
(33-c) * t = 300
going downstream (with the current), the equation is:
(33+c) * t = 360
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remove parentheses in both equations:
33*t - c*t = 300
33*t + c*t = 360
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add both equations together to remove c*t.
66*t = 660
t = 10
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substitute 10 for t in the first equation:
33*10 - c*10 = 300
330 - c*10 = 300
subtract 300 from both sides of equation to get:
30 - c*10 = 0
add c*10 to both sides of equation to get:
30 = c*10
divide both sides of equation by 10 to get:
3 = c
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substitute 10 for t and 3 for c in the second equation to get:
33*10 + 3*10 = 360
330 + 30 = 360
360 = 360
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equations are good.
answer is:
current is traveling at 3 miles per hour.

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