SOLUTION: A motorboat, whose speed in still water is 15 km/hour, traveled with the current of a river for 35 km, and against the current for 25 km. The boat took the same time traveling

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Question 972182:
A motorboat, whose speed in still water is 15 km/hour, traveled with the current of a river for 35 km, and against the current for 25 km. The boat took the same time traveling with the current as it did traveling against the current. What is the speed of the current in the river?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +c+ = the speed of the current in km/hr
Let +t+ = time in hrs going both ways
+15+%2B+c+ = speed of boat going with the current
+15+-+c+ = speed of boat going against the current
------------------------------------------------
Going with the current:
(1) +35+=+%28+15+%2B+c+%29%2At+
Going against the current:
(2) +25+=+%28+15+-+c+%29%2At+
-----------------------
(1) +t+=+35%2F%28+15+%2B+c+%29+
Substitute (1) into (2)
(2) +25+=+%28+15+-+c+%29%2A%28+35%2F%28+15+%2B+c+%29+%29+
(2) +25%2A%28+15+%2B+c+%29+=+35%2A%28+15+-+c+%29+
(2) +375+%2B+25c+=+525+-+35c+
(2) +60c+=+150+
(2) +c+=+2.5+
The speed of the current is 2.5 km/hr
-----------------------------------
check:
(1) +35+=+%28+15+%2B+2.5+%29%2At+
(1) +35+=+17.5t+
(1) +t+=+2+ hrs
------------------
(2) +25+=+%28+15+-+2.5+%29%2At+
(2) +25+=+12.5t+
(2) +t+=+2+ hrs
OK