SOLUTION: I need help setting up this Linear Equation: While on vacation, Kevin went for a swim in a nearby lake. Swimming against the current, it took him 8 minutes to swim 200 meters.

Question 581128: I need help setting up this Linear Equation: While on vacation, Kevin went for a swim in a nearby lake. Swimming against the current, it took him 8 minutes to swim 200 meters. Swimming back to shore with the current took half as long. Find Kevin's average swimming speed and the speed of the lake's current.
Found 2 solutions by dfrazzetto, mananth:
Answer by dfrazzetto(283) (Show Source): You can put this solution on YOUR website!
d=rt
200 = (r-c)8
200 = (r+c)4
r - c = 25
r + c = 50
-------------
2r = 75
r = 37.5
c = 12.5 m/min
average swimming speed = total distance / total time = 400/12 = 33 1/3 m/min
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
swimming speed =x mph
current speed =y mph
againstcurrent x-y 8 minutes
with current x+y 4 minutes

Distance = 200 m distance= 200
t=d/r against current
200.00 / ( x - y )= 8.00

8.00 x -8.00 y = 200.00 ....................1

200.00 / ( x + y )= 4.00
4.00 ( x + y ) = 200.00
4.00 x + 4.00 y = 200.00 ...............2
Multiply (1) by 1.00
Multiply (2) by 2.00
we get
8.00 x -8.00 y = 200.00
8.00 x + 8.00 y = 400.00
16.00 x = 600.00
/ 16.00
x = 37.5 Meters /minute

plug value of x in (1)
8 x -8 y = 200
300 -8 y = 200
-8 y = 200 -300
-8 y = -100
y = 12.5 Meters / minute
swimming speed 37.5 Meters /minute (0.63m/s)
current current 12.5 Meters /minute (0.21m/s)

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