SOLUTION: Can you help me set up a rational equation to solve this word problem algebraically please? If a boat goes downstream 78 miles in 3 1/4 hours and upstream 72 miles in 7 1/5 hour

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Question 882368: Can you help me set up a rational equation to solve this word problem algebraically please?
If a boat goes downstream 78 miles in 3 1/4 hours and upstream 72 miles in 7 1/5 hours. Find the speed of the boat in still water and the speed of the current.
Thank you.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = the speed of the boat in still water
Let +c+ = the speed of the current
+s+%2B+c+ = the speed of the boat going downstream
+s+-+c+ = the speed of the boat going upstream
---------------------------------------------
(1) +78+=+%28+s+%2B+c+%29%2A3.25+
(2) +72+=+%28+s+-+c+%29%2A7.2+
-----------------------
(1) +s+%2B+c+=+24+
(2) +s+-+c+=+10+
Add the equations
+2s+=+34+
+s+=+17+
and, since
(2) +s+-+c+=+10+
(2) +c+=+s+-+10+
(2) +c+=+17+-+10+
(2) +c+=+7+
The speed of the boat in still water is 17 mi/hr
The speed of the current is 7 mi/hr
-----------------
check:
(1) +78+=+%28+s+%2B+c+%29%2A3.25+
(1) +78+=+%28+17+%2B+7+%29%2A3.25+
(1) +78+=+24%2A3.25+
(1) +78+=+78+
You can check other equation