SOLUTION: Gertrude rows her boat 24 miles downstream in 4 hours. In order to make the return trip upstream in the same amount of time, the rate of the boat in still water was doubled. Find t

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Question 912742: Gertrude rows her boat 24 miles downstream in 4 hours. In order to make the return trip upstream in the same amount of time, the rate of the boat in still water was doubled. Find the rate of the current and the rate that Gertrude was rowing downstream.


Can you please hell me. I don't understand this problem.
Found 3 solutions by josgarithmetic, richwmiller, stanbon:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
Uniform Rates for Travel, RT=D rate time distance

Let r be the rate Gertrude would row if no river current
Let c be the rate of the river, the rate of flow of the river current

_________________rate________time__________distance
DOWNSTREAM_______r+c____________4_____________24
UPSTREAM_________2r-c___________4_____________24

Note very carefully, "the rate of the boat in still water was doubled".

Downstream Equation: %28r%2Bc%29%2A4=24
Simplify: r%2Bc=6
Upstream Equation: %282r-c%29%2A4=24
Simplify: 2r-c=6

Solve this system for r and c:
highlight%28system%28r%2Bc=6%2C2r-c=6%29%29

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
See
http://www.algebra.com/algebra/homework/word/travel/Travel_Word_Problems.faq.question.451884.html

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Gertrude rows her boat 24 miles downstream in 4 hours. In order to make the return trip upstream in the same amount of time, the rate of the boat in still water was doubled. Find the rate of the current and the rate that Gertrude was rowing downstream.
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Downstream DATA:
dist = 24 miles : time = 4 hrs ; rate = 24/4 = 6 mph
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Upstream DATA:
dist = 24 miles ; time = 4 hrs ; rate = 24/4 = 6 mph
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Equations:
b + c = 6
2b -c = 6
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Add and solve for "b":
3b = 12
b = 4 mph (rate of the boat in still water)
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Solve for "c":
b + c = 6
4 + c = 6
c = 2 mph (original current rate)
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Cheers,
Stan H.
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