SOLUTION: The rate of a boat in still water is 7km/hr. If the boat can travel 30km downstream in the same time it can travel 12 km upstream, find the rate of the river current. Is there a

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Question 1011286: The rate of a boat in still water is 7km/hr. If the boat can travel 30km downstream in the same time it can travel 12 km upstream, find the rate of the river current.
Is there a formula for this kind of question? Please help!

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
It's not really a "formula"
It's just catching on to a method
Just use [ distance ] = [ rate ] x [ time ]
--------------------------
Let +c+ = the rate of the current in km/hr
+7+%2B+c+ = rate of the boat going downstream
+7+-+c+ = rate of the boat going upstream
Let +t+ = time in hrs for going either upstream or downstream
------------------------------------
Equation for going downstream:
(1) +30+=+%28+7+%2B+c+%29%2At+
Equation for going upstream:
(2) +12+=+%28+7+-+c+%29%2At+
----------------------------
(1) +t+=+30+%2F+%28+7+%2B+c+%29+
Substitute this into (2)
(2) +12+=+%28+7+-+c+%29%2A%28+30+%2F+%28+7+%2B+c+%29+%29+
Multiply both sides by +7+%2B+c+
(2) +12%2A%28+7+%2B+c+%29+=+30%2A%28+7+-+c+%29+
(2) +84+%2B+12c+=+210+-+30c+
(2) +42c+=+126+
(2) +c+=+3+
The rate of the current is 3 km/hr
-----------------------------
check:
(1) +30+=+%28+7+%2B+c+%29%2At+
(1) +30+=+%28+7+%2B3+%29%2At+
(1) +30+=+10t+
(1) +t+=+3+
and
(2) +12+=+%28+7+-+c+%29%2At+
(2) +12+=+%28+7+-+3+%29%2At+
(2) +12+=+4t+
(2) +t+=+3+
OK