Question 840724
A motorboat can go 12 miles downstream on a river in 20 minutes.
 It takes 30 minutes for this boat to go back upstream the same 12 miles.
 Find the speed of the current.
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The idea is to understand what's going on here
We probably want the speeds in mph, therefore
change 20 min to 1/3 of an hr
change 30 min to 1/2 hr
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let s = the speed of the boat in still water
let c = rate of the current
then
(s+c) = effective speed down stream
and
(s-c) = effective speed upstream
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Write a distance equation for each way; dist = speed * time
{{{1/3}}}(s+c) = 12; downstream
{{{1/2}}}(s-c) = 12; upstream
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Simplify this, multiply the 1st equation by 3, the 2nd equation by 2
s + c = 36
s - c = 24
---------------Adding eliminates c, find s
2s = 60
s = 60/2
s = 30 mph in still water
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But they want the speed of the current
s + c = 36
replace s with 30
30 + c = 36
c = 36 - 30
c = 6 mph is the current
:
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Check this in the 1st original equation
{{{1/3}}}(30+6) =  
{{{1/3}}}* 36 = 12
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You can confirm this in the 2nd original equation
{{{1/2}}}(s-c) = 
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Is this starting to make sense to you now?