SOLUTION: A boat travels 30 miles upstream in three hours. It makes the return trip in one and a half hours. What is the speed of the boat in still water?

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Question 883918: A boat travels 30 miles upstream in three hours. It makes the return trip in one and a half hours. What is the speed of the boat in still water?
Found 2 solutions by Alan3354, josmiceli:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Use d = r*t, r = d/t to find the speed up and downstream.
The boat's speed is the average of the 2.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = the speed of the boat in still water
Let +c+ = the speed of the current
------------------
Going upstream:
(1) +30+=+%28+s+-+c+%29%2A3+
Going downstream:
(2) +30+=+%28+s+%2B+c+%29%2A1.5+
-----------------------
(1) +3s+-+3c+=+30+
(2) +1.5s+%2B+1.5c+=+30+
-----------------------
(1) +s+-+c+=+10+
(2) +15s+%2B+15c+=+300+
-----------------------
Multiply both sides of (1) by +15+
and add the equations
(1) +15s+-+15c+=+150+
(2) +15s+%2B+15c+=+300+
-----------------------
+30s+=+450+
+s+=+15+
------------
The speed of the boat in still water is 15 mi/hr
check:
(1) +s+-+c+=+10+
(1) +15+-+c+=+10+
(1) +c+=+5+
and
(2) +30+=+%28+s+%2B+c+%29%2A1.5+
(2) +30+=+%28+15+%2B+5+%29%2A1.5+
(2) +30+=+20%2A1.5+
(2) +30+=+30+
OK