SOLUTION: Port and Starboard are paddling canoes. They travel 20 miles downstream in 4 hrs. They return upstream in 6 hrs. A. How fast is the current? B. How fast can they paddle in still

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Port and Starboard are paddling canoes. They travel 20 miles downstream in 4 hrs. They return upstream in 6 hrs. A. How fast is the current? B. How fast can they paddle in still      Log On


   

Question 774491: Port and Starboard are paddling canoes. They travel 20 miles downstream in 4 hrs. They return upstream in 6 hrs.
A. How fast is the current?
B. How fast can they paddle in still water?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +c+ = the speed of the current
Let +s+ = their speed paddling in still water
--------------
Equation for going downstream:
(1) +20+=+%28+s+%2B+c+%29%2A4+
Equation for going upstream:
(2) +20+=+%28+s+-+c+%29%2A6+
--------------------
(1) +4s+%2B+4c+=+20+
(1) +s+%2B+c+=+5+
and
(2) +6s+-+6c+=+20+
(2) +3s+-+3c+=+10+
------------------
Multiply both sides of (1) by +3+
and add the equations
(2) +3s+-+3c+=+10+
(1) +3s+%2B+3c+=+15+
+6s+=+25+
+s+=+4.167+ mi/hr
and
(1) +s+%2B+c+=+5+
(1) +4.167+%2B+c+=+5+
(1) +c+=+.833+ mi/hr
--------------------
check:
(1) +20+=+%28+s+%2B+c+%29%2A4+
(1) +20+=+%28+4.167+%2B+.833+%29%2A4+
(1) +20+=+5%2A4+
(1) +20+=+20+
and
(2) +20+=+%28+s+-+c+%29%2A6+
(2) +20+=+%28+4.167+-+.833+%29%2A6+
(2) +20+=+3.333%2A6+
(2) +20+=+20+
OK