Question 249485
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.