SOLUTION: a boat went 15 miles downstream in 1 hour and then returned to its dock in 5/3 hours. if the current of the stream was constant, find the speed of the boat and speed of the current

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Question 584651: a boat went 15 miles downstream in 1 hour and then returned to its dock in 5/3 hours. if the current of the stream was constant, find the speed of the boat and speed of the current
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
+s+%2B+c+ = the speed of the boat going with the current
+s+-+c+ = the speed of the boat going against the current
--------
(1) +15+=+%28+s+%2B+c+%29%2A1+
(2) +15+=+%28+s+-+c+%29%2A%285%2F3%29+
---------------------
(1) +s+%2B+c+=+15+
and
(2) +s+-+c+=+%283%2F5%29%2A15+
(2) +s+-+c+=+9+
Add the equations
(1) +s+%2B+c+=+15+
(2) +s+-+c+=+9+
+2s+=+24+
+s+=+12+
and, since
(1) +s+%2B+c+=+15+
(1) +12+%2B+c+=+15+
(1) +c+=+3+
The speed of the boat in still water is 12 mi/hr
The speed of the current is 3 mi/hr
check:
(2) +15+=+%28+12+-+3+%29%2A%285%2F3%29+
(2) +15+=+9%2A%285%2F3%29+
(2) +15+=+15+
OK