SOLUTION: Chance paddled a canoe 10 miles upstream in a river that has a current of 4 mph. He then turned around and paddled downstream until he reached his original starting place. If the e

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Question 679635: Chance paddled a canoe 10 miles upstream in a river that has a current of 4 mph. He then turned around and paddled downstream until he reached his original starting place. If the entire trip took him 7 hours, how fast would Chance paddle 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
+s+%2B+4+ = speed of canoe going downstream
+s+-+4+ = speed of canoe going upstream
Let +t+ = time to go upstream
+7+-+t+ = time to go downstream
------------------
Equation for going upstream:
(1) +10+=+%28+s+-+4+%29%2At+
Equation for going downstream:
(2) +10+=+%28+s+%2B+4+%29%2A%28+7+-+t+%29+
--------------------------
(1) +t+=+10+%2F+%28+s+-+4+%29+
and
(2) +10+=+7s+%2B+28+-+s%2At+-+4t+
(2) +10+=+7s+%2B+28+-+t%2A%28+s+%2B+4+%29+
Substitute (1) into (2)
(2) +10+=+7s+%2B+28+-+%28+10+%2F+%28+s+-+4+%29+%29%2A%28+s+%2B+4+%29+
(2) +7s+%2B+18+=+++%28+10+%2F+%28+s+-+4+%29+%29%2A%28+s+%2B+4+%29+
Multiply both sides by +s+-+4+
(2) +%28+s+-+4+%29%2A%28+7s+%2B+18+%29+=+10s+%2B+40+
(2) +7s%5E2+-+28s+%2B+18s+-+72+=+10s+%2B+40+
(2) +7s%5E2+-+20s+-112+=+0+
Use quadratic formula
+s+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+7+
+b+=+-20+
+c+=+-112+
+s+=+%28+-%28-20%29+%2B-+sqrt%28+%28-20%29%5E2+-+4%2A7%2A%28-112%29+%29%29+%2F+%282%2A7%29+
+s+=+%28+20+%2B-+sqrt%28+400+%2B+3136+%29%29+%2F+14+
+s+=+%28+20+%2B+sqrt%28+3536+%29%29+%2F+14+
+s+=+%28+20+%2B+59.464+%29+%2F+14+
+s+=+79.464+%2F+14+
+s+=+5.676+
The speed in still water is 5.676 mi/hr
check answer:
(1) +10+=+%28+s+-+4+%29%2At+
(1) +10+=+%28+5.676+-+4+%29%2At+
(1) +10+=+1.676%2At+
(1) +t+=+5.967+ hrs
-------------------
(2) +10+=+%28+s+%2B+4+%29%2A%28+7+-+5.967+%29+
(2) +10+=+%28+s+%2B+4+%29%2A1.033+
(2) +9.681+=+s+%2B+4+
(2) +s+=+5.681+
----------------
This is pretty close. Error could be
due to rounding off. I think the method
is correct anyway.