SOLUTION: A motorboat travels 145 km in 5 hours going upstream. It travels 205 going downstream in the same amount of time. What is the rate of the boat in still water and what is the rate

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Question 1144623: A motorboat travels 145 km in 5 hours going upstream. It travels 205 going downstream in the same amount of time. What is the rate of the boat in still water and what is the rate of the current?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +r+ = rate of boat in still water
Let +c+ = rate of current
----------------------------------
Equation for going upstream ( against the current )
(1) +145+=+%28+r+-+c+%29%2A5+
Equation for going downstream ( with the current )
(2) +205+=+%28+r+%2B+c+%29%2A5+
--------------------------------
(1) +29+=+r+-+c+
(2) +41+=+r+%2B+c+ Add the equations
-------------------------
+70+=+2r+
+r+=+35+ mi/hr
--------------------------
Plug this result back into either equation
(1) +145+=+%28+35+-+c+%29%2A5+
(1) +29+=+35+-+c+
(1) +c+=+35+-+29+
(1) +c+=+6+ mi/hr
---------------------------
check:
(2) +205+=+%28+r+%2B+c+%29%2A5+
(2) +205+=+%28+35+%2B+6+%29%2A5+
(2) +205+=+41%2A5+
(2) +205+=+205+
OK