SOLUTION: A motorboat takes 4 hours to travel 320 mi going upstream. The return trip takes hours 2 going downstream. What is the rate of the boat in still water and what is the rate of th

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Question 299982:
A motorboat takes 4 hours to travel 320 mi going upstream. The return trip takes hours 2 going downstream. What is the rate of the boat in still water and what is the rate of the current?

Found 2 solutions by stanbon, josmiceli:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A motorboat takes 4 hours to travel 320 mi going upstream. The return trip takes hours 2 going downstream. What is the rate of the boat in still water and what is the rate of the current?
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Upstream rate: 320/4 = 80 mph
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Downstream DATA:
Your downstream rate is not clear.
====================================
Cheers,
Stan H.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let r%5Bs%5D = rate of boat in still water
Let r%5Bc%5D = rate of the current
Write 2 equations, one for upstream and one for downstream
given:
t%5Bu%5D+=+4 hrs
t%5Bd%5D+=+2 hrs
d=+320 mi
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upstream:
d+=+r%5Bu%5D%2At%5Bu%5D
d+=+%28r%5Bs%5D+-+r%5Bc%5D%29%2At%5Bu%5D
(1) 320+=+%28r%5Bs%5D+-+r%5Bc%5D%29%2A4
downstream:
d+=+r%5Bd%5D%2At%5Bd%5D
d+=+%28r%5Bs%5D+%2B+r%5Bc%5D%29%2At%5Bd%5D
(2) 320+=+%28r%5Bs%5D+%2B+r%5Bc%5D%29%2A2
-----------------
(1) r%5Bs%5D+-+r%5Bc%5D+=+80
(2) r%5Bs%5D+%2B+r%5Bc%5D+=+160
Add the equations
2r%5Bs%5D+=+240
r%5Bs%5D+=+120 mi/hr
And, since
(1) r%5Bs%5D+-+r%5Bc%5D+=+80
120+-+r%5Bc%5D+=+80
r%5Bc%5D+=+40 mi/hr
The rate of the boat in still water is120 mi/hr
The rate of the current is 40 mi/hr
check:
(1) 320+=+%28r%5Bs%5D+-+r%5Bc%5D%29%2A4
320+=+%28120+-+40%29%2A4
320+=+320
and
(2) 320+=+%28r%5Bs%5D+%2B+r%5Bc%5D%29%2A2
320+=+%28120+%2B+40%29%2A2
320+=+320
OK