SOLUTION: One more question please ! Someone please help. A boat can travel 10 miles downstream in 70 minutes. The return trip upstream requires 2 hours. Find the rate of the boat and rate

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Question 692747: One more question please !
Someone please help.
A boat can travel 10 miles downstream in 70 minutes. The return trip upstream requires 2 hours. Find the rate of the boat and rate of the current.
:(
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +c+ = the rate of the current in mi/hr
Let +b+ = the rate of the boat in still water in mi/hr
+b+%2B+c+ = the rate of the boat going downstream in mi/hr
+b+-+c+ = the rate of the boat going upstream in mi/hr
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Convert +70+ min to hrs.
+70%2F60+=+7%2F6+ hrs
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Equation for going downstream:
(1) +10+=+%28+b+%2B+c+%29%2A%287%2F6%29+
Equation for going upstream:
(2) +10+=+%28+b+-+c+%29%2A2+
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This is 2 equations with 2 unknowns, so it's solvable
(2) +10+=+2b+-+2c+
(2) +5+=+b+-+c+
(2) +b+=+c+%2B+5+
Substitute this into (1)
(1) +10+=+%28+c+%2B+5+%2B+c+%29%2A%287%2F6%29+
(1) +10+=+%28+2c+%2B+5+%29%2A%287%2F6%29+
(1) +10+=+%287%2F3%29%2Ac+%2B+35%2F6+
(1) +%287%2F3%29%2Ac+=+60%2F6+-+35%2F6+
(1) +%2814%2F6%29%2Ac+=+25%2F6+
(1) +14c+=+25+
(1) +c+=+25%2F14+
(1) +c+=+1.7857+
and, since
(2) +b+=+c+%2B+5+
(2) +b+=+1.7857+%2B+5+
(2) +b+=+6.7857+
The rate of the boat is 6.7857 mi/hr
The rate of the current is 1.7857 mi/hr
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check:
(2) +10+=+%28+b+-+c+%29%2A2+
(2) +10+=+%28+6.7857+-+1.7857+%29%2A2+
(2) +10+=+5%2A2+
(2) +10+=+10+
OK
(1) +10+=+%28+b+%2B+c+%29%2A%287%2F6%29+
(1) +10+=+%28+6.7857+%2B+1.7857+%29%2A%287%2F6%29+
(1) +10+=++8.5714%2A%287%2F6%29+
(1) +60+=+8.5714%2A7+
(1) +60+=+59.9998+
error must be due to rounding off- OK