SOLUTION: A woman rows a boat upstream form one point on a river to another point 12km away in 1 and half hours. The return trip with the current takes only 40 minutes. How fast would she be

Question 730127: A woman rows a boat upstream form one point on a river to another point 12km away in 1 and half hours. The return trip with the current takes only 40 minutes. How fast would she be rowing if she were rowing in still water (as if there is no current), and what speed is the current flowing ?
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
Boat speed speed =x mph
current speed =y mph
against current 1.5 hours
with current 2/ 3 hours

Distance with current 12 miles distance against current 12
t=d/r against current (x-y)
12.00 / ( x - y )= 1.50

1.50 x - -1.50 y = 12.00 ....................1
with current (x+y)
12.00 / ( x + y )= 2/3
2/3 ( x + y ) = 12.00
2/3 x + 2/3 y = 12.00
2x+2y=36
x+y=18........................(2)
multiply equation (1) by 2
we get3x-3y=24
multiply equation (2) by 3
3x+3y=54
add up the equations
6x=78
x=13 km/h the speed of boat in stll water
plug x in the equation x+y=18
y=5km/h the current speed
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