SOLUTION: I am struggling in the set up of this problem. Can you please help me? The current in a bayou near Lafayette is 4 miles per hour. A paddleboat travels 48 miles up stream in the

Algebra ->  Expressions-with-variables -> SOLUTION: I am struggling in the set up of this problem. Can you please help me? The current in a bayou near Lafayette is 4 miles per hour. A paddleboat travels 48 miles up stream in the      Log On


   

Question 509721: I am struggling in the set up of this problem. Can you please help me?
The current in a bayou near Lafayette is 4 miles per hour. A paddleboat travels 48 miles up stream in the same amount of time it takes to travel 72 miles downstream. Find the speed of the boat in still water.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let s = speed of boat in still water
Let t = time it takes to go either upstream or downstream
+c+=+4+ is the speed of the current
+s+%2B+c+ is the boat's speed going downstream
+s+-+c+ is the boat's speed going upstream
------------
given:
Going upstream:
(1) +48+=+%28s+-+4%29%2At+
Going downstream:
(2) +72+=+%28s+%2B+4%29%2At+
-------------------
(1) +48+=+s%2At+-+4t+
and
(2) +72+=+s%2At+%2B+4t+
Subtract (1) from (2)
(2) +72+=+s%2At+%2B+4t+
(1) +-48+=+-s%2At+%2B+4t+
+24+=+8t+
+t+=+3+
By substitution:
(1) +48+=+%28s+-+4%29%2A3+
(1) +48+=+3s+-+12+
(1) +3s+=+60+
(1) +s+=+20+
The speed in still water is 20 mi/hr
check answer:
(2) +72+=+%2820+%2B+4%29%2A3+
(2) +72+=+24%2A3+
(2) +72+=+72+
OK