SOLUTION: A riverboat cruise upstream on a river, takes 8 hr and covers 224 mi. The return trip downstream with the current takes only 7 hr. Find the speed of the riverboat in still water an

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Question 927488: A riverboat cruise upstream on a river, takes 8 hr and covers 224 mi. The return trip downstream with the current takes only 7 hr. Find the speed of the riverboat in 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+ = the speed of the boat in still water in mi/hr
Let +c+ = the speed of the current in mi/hr
-----------------
+s+-+c+ = the speed of the boat going upstream
+s+%2B+c+ = the speed of the boat going downstream
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Equation for going upstream:
(1) +224+=+%28+s+-+c+%29%2A8+
Equation for going downstream:
(2) +224+=+%28+s+%2B+c+%29%2A7+
-----------------------
(1) +8s+-+8c+=+224+
(2) +7s+%2B+7c+=+224+
-----------------------
(1) +s+-+c+=+28+
(2) +s+%2B+c+=+32+
Add the equations
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+2s+=+60+
+s+=+30+
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(1) +30+-+c+=+28+
(1) +c+=+2+
---------------
The speed of the boat in still water is 30 mi/hr
The speed of the current is 2 mi/hr
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check:
(1) +224+=+%28+30+-+2+%29%2A8+
(1) +224+=+224+
OK
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