Question 249485: larry takes 1 1/2 times as long to go 72 miles upstream as he takes to go 72 miles downstream. if the speed of his boat in still water is 30 mph, what is the speed of the current?
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! time going upstream = 1.5 * time going downstream
distance = 72 miles
rate in still water (no current) = 30 mph
What is the current?
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Recall d=rt, where d=distance, r=rate, and t=time.
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We can set the upstream leg of the trip as:
72 = (30-x)*1.5
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The downstream leg of the trip is:
72 = (30+x)*1
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Since the distances are equal, we can set the right-hand sides to equal each other.
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(30-x)*1.5 = 30+x
45 - 1.5x = 30 + x
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Subtracting adding 1.5x to both sides...
45 = 30 + 2.5x
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Subtracting 30 from both sides...
15 = 2.5x
so
2.5x = 15
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Divide both sides by 2.5...
x = 15/2.5 = 6
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So our proposed speed of the current = 6 mph.
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Checking our work
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The upstream leg would have a speed against the current of 24 mph. Traveling 72 miles would take 72/24 = 3 hr.
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The downstream leg would have a speed assisted by the current of 36 mph. Traveling the 72 miles would take 72/36 = 2 hr.
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Thus the roundtrip would be 5 hrs.
The total distance traveled would be 144 miles.
So the average speed would be be 144/5 = 28.8 mph
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Done.
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