SOLUTION: A boat takes a trip upriver against the current in 6 hours. Coming back down river, the boat can travel 6 mph faster and makes the trip in 4 hours. What is the speed of the boat

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Question 760024: A boat takes a trip upriver against the current in 6 hours. Coming back down river, the boat
can travel 6 mph faster and makes the trip in 4 hours. What is the speed of the boat in still
water?
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 upriver
+s+%2B+c+ = the speed of the boat going downriver
Let +d+ = the one-way distance the boat travels
------------------
Going upriver:
(1) +d+=+%28+s+-+c+%29%2A6+
Going downriver:
(2) +d+=+%28+s+%2B+c+%29%2A4+
and, also given:
(3) +s+%2B+c+=+s+-+c+%2B+6+
---------------------
(3) +c+=+-c+%2B+6+
(3) +2c+=+6+
(3) +c+=+3+ mi/hr
-------------------
By substitution:
(2) +%28+s-c+%29%2A6+=+%28+s+%2B+c+%29%2A4+
(2) +%28+s-3+%29%2A6+=+%28+s+%2B+3+%29%2A4+
(2) +6s+-+18+=+4s+%2B+12+
(2) +2s+=+30+
(2) +s+=+15+
The speed of the boat in still water is 15 mi/hr
check:
(1) +d+=+%28+s+-+c+%29%2A6+
(1) +d+=+%28+15+-+3+%29%2A6+
(1) +d+=+72+ mi
and
(2) +d+=+%28+s+%2B+c+%29%2A4+
(2) +d+=+%28+15+%2B+3+%29%2A4+
(2) +d+=+72+ mi
OK