SOLUTION: The current in the Sauk Riber moves at a rate of 2 mph. Mias canoe can go 18 miles upstream in the same amount of time it takes to go 30 miles downstream. Find the speed of the can
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Question 666093: The current in the Sauk Riber moves at a rate of 2 mph. Mias canoe can go 18 miles upstream in the same amount of time it takes to go 30 miles downstream. Find the speed of the canoe in still water.
It says to make a chart such as
D R T
upstream
downstream
Answer by DrBeeee(684) (Show Source): You can put this solution on YOUR website!
Here's a chart.
Let c = canoe speed mph
Let t = time it takes
*
....leg of travel............rate...........time...........distance........
*
......upstream..............(c-2).............t..............18.............
*
.....downstream.............(c+2).............t..............30.............
*
*
Now use the basic formula for distance
(1) d = r*t
and solve for t and get
(2) t = d/r
Now use (2) for each of the legs and get
(3) t = 18/(c-2) for upstream and
(4) t = 30/(C+2) for downstream
Since the time is the same we can equate (3) and (4) and get
(5) 18/(c-2) = 30/(c+2) or by cross multiplying we have
(6) 18*(c+2) = 30*(c-2) or
(7) 18c + 36 = 30c - 60 or
(8) 96 = 12c or
(9) c = 8
Is this correct? Let's check using (1)
Is (18 = (8-2)t)?
Is (18 = 6t)?
Is (3 = t)?
Is (30 = (8+2)t)?
Is (30 = 10t)?
Is (3 = t)?
Since we get t = 3 for each leg we are correct.
Answer: The canoe travels at 8 mph in still water.
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