<PRE><B>Question 446497</B>
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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