SOLUTION: A motorboat can go 16 miles downstream on a river in 20 minutes. It takes 30 minutes for this boat to go back upstream the same 16 miles. Find the speed of the boat in still water.

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Question 947446: A motorboat can go 16 miles downstream on a river in 20 minutes. It takes 30 minutes for this boat to go back upstream the same 16 miles. 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!
+20%2F60+=+1%2F3+ hrs
+30%2F60+=+1%2F2+ hrs
Let +s+ = the speed of the boat in still water in mi/hr
Let +c+ = the speed of the current in mi/hr
----------------------------------
Going downstream:
(1) +16+=+%28+s+%2B+c+%29%2A%281%2F3%29+
Going upstream:
(2) +16+=+%28+s+-+c+%29%2A%281%2F2%29+
-------------------------
(1) +s+%2B+c+=+48+
(2) +s+-+c+=+32+
------------------
Add the equations
+2s+=+80+
+s+=+40+
and
(1) +40+%2B+c+=+48+
(1) +c+=+8+
----------------
The speed of the boat in still water is 40 mi/hr
check:
(2) +s+-+c+=+32+
(2) +40+-+8+=+32+
(2) +32+=+32+
OK