SOLUTION: A crew rowed 7 miles upstream in 2 hours and the 6 1/2 miles downstream in 1 hour. Find the rate of the crew in still water and the rate of the current.
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Question 1111037: A crew rowed 7 miles upstream in 2 hours and the 6 1/2 miles downstream in 1 hour. Find the rate of the crew in still water and the rate of the current. Found 2 solutions by josgarithmetic, ikleyn:Answer by josgarithmetic(39617) (Show Source):
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A crew rowed 7 miles upstream in 2 hours and the 6 1/2 miles downstream in 1 hour. Find the rate of the crew in still water and the rate of the current.
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A crew rowed U miles upstream in h hours and the D miles downstream in k hour. Find the rate of the crew in still water and the rate of the current.
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r, speed of crew if no current
c, speed of the current
U=7
D=6.5
h=2
k=1
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and
You can just substitute the values to compute r and c.
Let "u" be the speed of the boat in still water (in mph)
and "v" be the speed of the current.
Then the effective speed upstream is
u - v = 3.5 mph (1) (=7/2 mph)
while the effective speed downstream is
u + v = 6.5 mph (2) (from the condition)
Adding (1) and (2), you find 2u = 3.5+6.5 = 10 ====> u = 5 mph.
Then from (2), v = 6.5 - 5 = 1.5 mph.
Solved.
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It is a typical and standard Upstream and Downstream round trip word problem.
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