SOLUTION: Okay this is the problem and i need to use elimination or substitution to solve. I have no idea how to get the equations. A motorboat can go 12 miles downstream on a river in 20

Question 840724: Okay this is the problem and i need to use elimination or substitution to solve. I have no idea how to get the equations.
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.
(btw it won't let me choose a topic)
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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.
:
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
:
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
:
Write a distance equation for each way; dist = speed * time
(s+c) = 12; downstream
(s-c) = 12; upstream
:
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
:
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
:
:
Check this in the 1st original equation
(30+6) =
* 36 = 12
:
You can confirm this in the 2nd original equation
(s-c) =
:
:
Is this starting to make sense to you now?

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