SOLUTION: A boat takes 3 hours longer to go 60 miles up a river than to return. If the boat cruises at 15mph in still water, what is the rate of the current? Also, what level of Algebraic pr

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Question 794073: A boat takes 3 hours longer to go 60 miles up a river than to return. If the boat cruises at 15mph in still water, what is the rate of the current? Also, what level of Algebraic problem solving is this considered?
Thanks,
Steve Schrock
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +c+ = the rate of the current
+15+-+c+ = rate going upriver
+15+%2B+c+ = rate going downriver
Let +t+ = time in hours to go downriver
+t+%2B+3+ = time in hours to go upriver
----------------------------------
Equation for going upriver:
(1) +60+=+%28+15+-+c+%29%2A%28+t+%2B+3+%29+
Equation for going downriver:
(2) +60+=+%28+15+%2B+c+%29%2At+
----------------------
(1) +60+=+15t+-+c%2At+%2B+45+-+3c+
(1) +15+=+15t+-+c%2A%28+t+%2B+3+%29+
(1) +c%2A%28+t+%2B+3+%29+=+15%2A%28+1+-+t+%29+
(1) +c+=+15%2A%28+1+-+t+%29+%2F+%28+t+%2B+3+%29+
and
(2) +60+=+15t+%2B+c%2At+
(2) +c+=+%28+60t+-+15+%29+%2F+t+
(2) +c+=+15%2A%28+4t+-+1+%29+%2F+t+
by substitution:
(1) +15%2A%28+4t+-+1+%29+%2F+t+=+15%2A%28+1+-+t+%29+%2F+%28+t+%2B+3+%29+
(1) +%28+4t+-+1+%29+%2F+t+=+%28+1+-+t+%29+%2F+%28+t+%2B+3+%29+
multiply both sides by +t%2A%28+t%2B3+%29+
(1) +%28+4t+-+1+%29%2A%28+t+%2B+3+%29+=+t%2A%28+-t+%2B+1+%29+
(1) +4t%5E2+-+t+%2B+12t+-+3++=+-t%5E2+%2B+t+
(1) +5t%5E2+%2B+10t+-+3+=+0+
Use the quadratic equation:
+t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+a+=+5+
+b+=+10+
+c+=+-3+
+t+=+%28-10+%2B-+sqrt%28+10%5E2-4%2A5%2A%28-3%29+%29%29%2F%282%2A5%29+
+t+=+%28-10+%2B-+sqrt%28+100+%2B+60+%29%29+%2F+10+
+t+=+%28-10+%2B-+sqrt%28+160+%29%29+%2F+10+
+t+=+%28+-10+%2B+4%2Asqrt%28+10+%29+%29%2F10+
+t+=+-1+%2B+%282%2F5%29%2Asqrt%2810%29+
You can finish this. Find t+, and then plug
value into (2) to find +c+
Hopefully, I didn't make a mistake.