SOLUTION: A boat traveled 230 miles downstream and back. The trip downstream took 10 hours. The trip back took 46 hours. Find the speed of the boat in the still water and the speed of the cu

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Question 919497: A boat traveled 230 miles downstream and back. The trip downstream took 10 hours. The trip back took 46 hours. Find the speed of the boat in the still water and the speed of the current
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = th speed of the boat in mi/hr
in still water
Let +c+ = the speed of the current in mi/hr
--------------
Equation for going downstream:
(1) +230+=+%28+s+%2B+c+%29%2A10+
Equation for going upstream:
(2) +230+=+%28+s+-+c+%29%2A46+
------------------------
(1) +10s+%2B+10c+=+230+
(2) +46s+-+46c+=+230+
------------------------
Add the equations:
(1) +s+%2B+c+=+23+
(2) +s+-+c+=+5+
------------------
+2s+=+28+
+s+=+14+
and, since
(1) +s+%2B+c+=+23+
(1) +14+%2B+c+=+23+
(1) +c+=+9+
The speed of the boat
is 14 mi/hr in still water
The speed of the current is 9 mi/hr
--------------
check:
(1) +230+=+%28+14+%2B+9+%29%2A10+
(1) +230+=+230+
OK -you can check other equation