SOLUTION: Looking over my daughter's 9th grade algebra homework and the answers seem correct though I can't figure out how she got there - and it looks like she probably doesn't know either.

Question 419568: Looking over my daughter's 9th grade algebra homework and the answers seem correct though I can't figure out how she got there - and it looks like she probably doesn't know either. Typical question:
Merle took half an hour to row 3km with the current. When he returned, he took 90 minutes. Find his rowing rate and the speed of the current.
I'm not sure how to set up the problem. Any help would be greatly appreciated. Thanks.
Found 2 solutions by ankor@dixie-net.com, mananth:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Merle took half an hour to row 3km with the current.
When he returned, he took 90 minutes.
Find his rowing rate and the speed of the current.
;
Since you probably want the speed in km/hr, change the times to hrs
.5 hrs and 1.5 hrs
:
Let r = his rowing speed in still water
Let c = rate of the current
then
(r+c) = his effective speed with the current
and
(r-c) = his effective speed against the current
:
Write a distance equation for each trip: time * speed = dist
.5(r+c) = 3; (downstream)
1.5(r-c) = 3; (upstream)
You can simplify both these equations, divide the 1st by .5, the 2nd by 1.5, results:
r + c = 6
r - c = 2
-------------adding these equations eliminates c, find r
2r = 8
r = 8/2
r = 4 km/hr is his rowing speed
:
Find the current using r + c = 6
4 + c = 6
c = 6 - 4
c = 2 km/hr is the current
:
:
Check solution in the 1st original equation
.5(4 + 2) = 3

Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
Merle took half an hour to row 3km with the current. When he returned, he took 90 minutes. Find his rowing rate and the speed of the current.
upstream time = 1.5 hours
downstream time= 0.5 hours

Distance = same
boat speed =x
current speed =y
t=d/r
3 / ( x - y )= 1.50
1.5 ( x - y ) = 3.00
1.5x-1.5 y = 3 ....................1
3 / ( x + y )= 0.5
0.5 ( x + y ) = 3
0.5 x + 0.5 y = 3 ...............2
Multiply (1) by 1
Multiply (2) by 3
we get
1.5 x + -1.5 y = 3
1.5 x + 1.5 y = 9
3 x = 12
/ 3
x = 4 mph boat speed

plug value of x in (1)
1.5 x -1.5 y = 3
6 -1.5 y = 3
-1.5 y = 3 -6
-1.5 y = -3
y = 2 mph current speed

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