Question 249957: A boat can travel 9mph in still water. It travels 7 miles downstream in the same time that it travels only 3 miles upstream. Find the rate of the current.
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! Start by setting up the variables you will need.
s = speed in still water = 9 mph
c = current
d = rt is the basic distance formula, where d=distance, r=rate, and t=time
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Now translate the English into math.
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Traveling downstream:
r = s+c The current adds to the boat's speed.
d=7 in time t
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Traveling upstream:
r = s - c The current subtracts from the boat's speed.
d =3 in time t
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We are told t=t so we can rearrange both equation to define 't'.
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7 = (s+c) * t
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Divide both sides by (s+c)
7/(s+c) = t
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The other equation is:
3 = (s-c) * t
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Divide both sides by (s-c)
3/(s-c) = t
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Since both equations = t, we can use this fact to set them equal to one another
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7/(s+c) = 3/(s-c)
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Cross multiply
7(s-c) = 3(s+c)
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7s - 7c = 3s + 3c
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4s = 10c
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Recall s = 9
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4(9) = 36 = 10c
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c = 3.6
The current runs at 3.6 mph
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Next substitute back into the original equations to see if this answer is correct.
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How long does it take to go 7 miles downstream?
7 = (9+3.6)t = 12.6t
t = 7/12.6 = .555555556
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3 = (9-3.6)t = 5.4t
t = 3/5.4 = .555555556
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So we can conclude the current of the river is 3.6 mph.
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Done
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