Question 446497: Suppose a boat that can travel 20 mph in still water takes a 72 mile trip downriver and back. Due to a higher river flow, the current for the downriver trip was 2 mph faster than for the return trip. If the total travel time was 7 hours, how fast did the river flow for the downstream trip? How fast did the river flow for the return trip? In both cases the river flowed in the same direction.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Suppose a boat that can travel 20 mph in still water takes a 72 mile trip downriver and back. Due to a higher river flow, the current for the downriver trip was 2 mph faster than for the return trip. If the total travel time was 7 hours, how fast did the river flow for the downstream trip? How fast did the river flow for the return trip? In both cases the river flowed in the same direction.
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Downstream DATA:
dist = 72 miles ; rate = 22+c mph ; time = 72/(22+c) hrs.
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Upstream DATA:
dist = 72 miles ; rate = 20-c mph ; time = 72/(20-c) hrs.
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Equation:
time + time = 7 hrs
72/(22+c)+72/(20-c) = 7
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72(20-c) + 72(22+c) = 7(22+c)(20-c)
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72*20 + 72*22 = 7(440-2c-c^2)
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7c^2+14c-56 = 0
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c^2 + 2c - 8 = 0
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(c+4)(c-2) = 0
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Positive solution:
current = 2 mph
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Cheers,
Stan H.
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