SOLUTION: A motorboat traveled 36 miles downstream, with the current, in 1.5 hours. The return trip upstream against the current, covered the same distance, but took two hours. Find the boat

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Question 520863: A motorboat traveled 36 miles downstream, with the current, in 1.5 hours. The return trip upstream against the current, covered the same distance, but took two hours. Find the boats rate in still water and the rate of the current.
I tried to figure this problem out, but had trouble making it into an equation. What would X and Y stand for in this case?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = boat's rate in still water
Let +c+ = rate of current
given:
+d+=+36+
+t%5B1%5D+=+1.5+
+t%5B2%5D+=+2+
-----------
Going downstream:
+d+=+%28+s+%2B+c+%29%2At%5B1%5D+
(1) +36+=+%28+s%2B+c+%29%2A1.5+
Going upstream:
+d+=+%28+s+-+c+%29%2At%5B2%5D+
(2) +36+=+%28+s+-+c+%29%2A2+
-----------------
(1) +36+=+1.5s+%2B+1.5c+
(1) +15s+%2B+15c+=+360+
(1) +s+%2B+c+=+24+
and
(2) +36+=+2s+-+2c+
(2) +s+-+c+=+18+
--------------
Add the equations
(1) +s+%2B+c+=+24+
(2) +s+-+c+=+18+
+2s+=+42+
+s+=+21+
and, since
(1) +s+%2B+c+=+24+
(1) +21+%2B+c+=+24+
(1) +c+=+3+
The boats rate in still water is 21 mi/hr
The rate of the current is 3 mi/hr
check:
(1) +36+=+%28+s%2B+c+%29%2A1.5+
(1) +36+=+%28+21%2B+3+%29%2A1.5+
(1) +36+=+24%2A1.5+
(1) +36+=+36+
OK