SOLUTION: Paddling a canoe with current you can go 12 miles in 2 hours,but against the current the return trip takes 6 hours paddling at the same rate.Find the rate of the current and the ra

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Paddling a canoe with current you can go 12 miles in 2 hours,but against the current the return trip takes 6 hours paddling at the same rate.Find the rate of the current and the ra      Log On


   

Question 742418: Paddling a canoe with current you can go 12 miles in 2 hours,but against the current the return trip takes 6 hours paddling at the same rate.Find the rate of the current and the rate of paddling in water with no current.Of course,assume the current rate remains the same.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Let the speed of paddling in still waters be x mph and speed of current be y mph
DOWNSTREAM
------------------------
if Distance=12mil and time=2h, then

Speed+=%28x%2By%29mph+=+Distance+%2F+time+=+12+%2F2+=+6

x%2B+y+=+6+...... eq.1

UPSTREAM
--------------------

Speed+=+%28x-y%29+mph+=+Distance+%2F+time+=+12%2F6+=+2

x+-y+=+2...... eq.2

eq.1 + eq.2

x%2B6%2Bx-6+=6%2B2

2x+=8

x+=+4mph, then

4mph%2B+y+=+6mph+

y+=+2mph........ ANSWER

CHECK

12+%2F+%284%2B2%29+=+2+hours

12+%2F+%28+4-2%29+=+6+hours