SOLUTION: An open water swimmer can swim 27 miles with an ocean current in the same amount of time it takes to swim nine miles against the same current. Find the speed of the current if the

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: An open water swimmer can swim 27 miles with an ocean current in the same amount of time it takes to swim nine miles against the same current. Find the speed of the current if the       Log On


   

Question 1128948: An open water swimmer can swim 27 miles with an ocean current in the same amount of time it takes to swim nine miles against the same current. Find the speed of the current if the swimmer can swim 4 miles per hour in still water
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the rate of the current = +c+
Swimmer's rate swimming with the current:
+4+%2B+c+
Swimmer's rate swimming against the current:
+4+-+c+
Let +t+ = time in hrs for both trips
---------------------------------------------
Swimming with the current:
(1) +27+=+%28+4+%2B+c+%29%2At+
Swimming against the current
(2) +9+=+%28+4+-+c+%29%2At+
------------------------------------
(1) +t+=+27%2F%28+4+%2B+c+%29+
(2) +t+=+9%2F%28+4+-+c+%29+
+27%2F%28+4+%2B+c+%29+=+9%2F%28+4+-+c+%29+
+27%2A%28+4+-+c+%29+=+9%2A%28+4+%2B+c+%29+
+3%2A%28+4+-+c+%29+=+4+%2B+c+
+12+-+3c+=+4+%2B+c+
+4c+=+8+
+c+=+2+
The speed of the current is 2 mi/hr
check:
(1) +t+=+27%2F%28+4+%2B+2+%29+
(1) +t+=+9%2F2+
and
+t+=+9%2F%28+4+-+2+%29+
+t+=+9%2F2+
OK