SOLUTION: If a boat can travel 30mph in still water, and can travel 9 miles downstram in the same time it takes 1 mile to go upstream, what is the rate of the rivers current?

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Question 795399: If a boat can travel 30mph in still water, and can travel 9 miles downstram in the same time it takes 1 mile to go upstream, what is the rate of the rivers current?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +c+ = the rate of the current in mi/hr
+30+%2B+c+ = boat's speed going downstream in mi/hr
+30+-+c+ = boat's speed going upstream in mi/hr
Let +t+ = the time in hours for both upstream and downstream
-----------------------
Equation for going downstream:
(1) +9+=+%28+30%2B+c+%29%2At+
Equation for going upstream:
(2) +1+=+%28+30+-+c+%29%2At+
--------------------
(1) +9+=+30t+%2B+c%2At+
and
(2) +1+=+30t+-+c%2At+
-------------------
Add the equations
+10+=+60t+
+t+=+1%2F6+
and
(1) +9+=+%28+30%2B+c+%29%2A%281%2F6%29+
(1) +54+=+30+%2B+c+
(1) +c+=+24+
The rate of the current is 24 mi/hr
check:
(2) +1+=+%28+30+-+c+%29%2At+
(2) +1+=+%28+30+-+24+%29%2A%281%2F6%29+
(2) +6+=+6+
and
(1) +9+=+%28+30%2B+c+%29%2At+
(1) +9+=+%28+30%2B+24+%29%2A%281%2F6%29+
(1) +54+=+54+
OK