SOLUTION: Please help me solve this equation : Paula rows a boat 6 miles upstream in 3 hours. She returns 6 miles downstream in 2 hours. What is the rate at which Paula rows in still water?

Question 695724: Please help me solve this equation : Paula rows a boat 6 miles upstream in 3 hours. She returns 6 miles downstream in 2 hours. What is the rate at which Paula rows in still water? What is the rate of the current?
Found 2 solutions by mananth, josmiceli:
Answer by mananth(16949) (Show Source): You can put this solution on YOUR website!
canoe speed speed =x mph
current speed =y mph
against current 3 hours
with current 2 hours

Distance with current 6 miles distance against current 6
t=d/r against current (x-y)
6.00 / ( x - y )= 3.00

3.00 x - -3.00 y = 6.00 ....................1
with current (x+y)
6.00 / ( x + y )= 2.00
2.00 ( x + y ) = 6.00
2.00 x + 2.00 y = 6.00 ...............2
Multiply (1) by 2.00
Multiply (2) by 3.00
we get
6.00 x + -6.00 y = 12.00
6.00 x + 6.00 y = 18.00
12.00 x = 30.00
/ 12.00
x = 2.5 mph

plug value of x in (1) y
3 x -3 y = 6
7.5 -3 -7.5 = 6
-3 y = 6
-3 y = -1.5 mph
y = 0.5
canoe speed 2.5 mph
current 0.5 mph

Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = her speed rowing in still water
Let = the rate of the current
= the speed of the boat going upstream
= the speed of the boat going downstream
-------------
Her equation for going upstream:
(1)
Her equation for going downstream:
(2)
-------------------
(1)
(1)
and
(2)
(2)
---------------
Add (1) and (2)
(1)
(2)

and,since
(1)
(1)
(1)
Paula rows 2.5 mi/hr is still water
The speed of the current is .5 mi/hr
check answers:
(1)
(1)
and
(2)
(2)
(2)
OK

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