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Question 189422: These two questions are bogging me down. Please help.
Upstream, downstream. Junior’s boat will go 15 miles per hour in still water. If he can go 12 miles downstream in the same amount of time as it takes to go 9 miles upstream, then what is the speed of the current.
Big plane. A six-passenger plane cruises at 180 mph in calm air. If the plane flies 7 miles with the wind in the same amount of time as it flies 5 miles against the wind, then what is the wind speed?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Junior’s boat will go 15 miles per hour in still water. If he can go 12 miles downstream in the same amount of time as it takes to go 9 miles upstream, then what is the speed of the current.
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Let the speed of the current be "c mph"
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Downstream DATA:
distance = 12 miles ; rate = (15 + c) mph ; time = 12/(15+c) hrs
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Upstream DATA;
distance = 9 miles ; rate = (15 - c) mph ; time = 9/(15-c) hrs
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Equation:
time = time
12/(15+c) = 9/(15-c)
4/(15+c) = 3/(15-c)
Cross-multiply to get:
4(15-c) = 3(15+c)
60 - 4c = 45 + 3c
7c = 15
c = (15/7) mph -------speed of the current
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A six-passenger plane cruises at 180 mph in calm air. If the plane flies 7 miles with the wind in the same amount of time as it flies 5 miles against the wind, then what is the wind speed?
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Let the wind speed be "w".
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With the wind DATA:
distance = 7 miles : rate = 180+w mph ; time = 7/(180+w) hrs
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Against the wind DATA:
distance = 5 miles ; rate = 180-w mph ; time = 5/(180-w) hrs
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Equation:
time = time
7/(180+w) = 5/(180-w)
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Solve for "w".
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Cheers,
Stan H.
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