SOLUTION: A boat can travel 36 miles downstream in 2 hours. Coming back upstream,, the boat takes 3 hours. What is the rate of the boat in still water? What is the rate of the current?

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A boat can travel 36 miles downstream in 2 hours. Coming back upstream,, the boat takes 3 hours. What is the rate of the boat in still water? What is the rate of the current?       Log On


   

Question 891914: A boat can travel 36 miles downstream in 2 hours. Coming back upstream,, the boat takes 3 hours. What is the rate of the boat in still water? What is the 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 +s+ = the speed of the boat in still water
----------------
Going downstream:
(1) +36+=+%28+s+%2B+c+%29%2A2+
Going upstream:
(2) +36+=+%28+s+-+c+%29%2A3+
---------------------
(1) +2s+%2B+2c+=+36+
(2) +3s+-+3c+=+36+
--------------------
(1) +s+%2B+c+=+18+
(2) +s+-+c+=+12+
Add the equations
+2s+=+30+
+s+=+15+
and
(1) +15+%2B+c+=+18+
(1) +c+=+3+
The rate of the boat in still water is 15 mi/hr
The speed of the current is 3 mi/hr
------------------
check:
(1) +36+=+%28+s+%2B+c+%29%2A2+
(1) +36+=+%28+15+%2B+3+%29%2A2+
(1) +36+=+18%2A2+
(1) +36+=+36+
and
(2) +36+=+%28+s+-+c+%29%2A3+
(2) +36+=+%28+15+-+3+%29%2A3+
(2) +36+=+12%2A3+
(2) +36+=+36+
OK