SOLUTION: A girl rows 11 km downstream in 2 h. Her return trip takes 3 h. How fast can she row in still water. in km/h?

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Question 843383: A girl rows 11 km downstream in 2 h. Her return trip takes 3 h. How fast can she row in still water. in km/h?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = her speed in still water in km/hr
Let +c+ = the speed of the current in km/hr
---------------------------------------
Equation for rowing downstream:
(1) +11+=+%28+s+%2B+c+%29%2A2+
Equation for rowing upstream:
(2) +11+=+%28+s+-+c+%29%2A3+
-----------------------------
This is 2 equations and 2 unknowns
so it's solvable
(1) +11+=+2s+%2B+2c+
and
(2) +11+=+3s+-+3c+
-----------------------
Multiply both sides of (1) by 3 and
both sides of (2) by 2
Then add the equations
(1) +6s+%2B+6c+=+33+
(2) +6s+-+6c+=+22+
+12s+=+55+
+s+=+4.5833+
She can row 4.5833 km/hr in still water
check:
(1) +2s+%2B+2c+=+11+
(1) +2%2A%2855%2F12%29+%2B+2c+=+11+
(1) +55%2F6+%2B+2c+=+11+
(1) +2c+=+66%2F6+-+55%2F6+
(1) +2c+=+11%2F6+
(1) +c+=+11%2F12+
(1) +c+=+.9167+
---------------------
(2) +3s+-+3c+=+11+
(2) +3%2A%2855%2F12%29+-+3%2A%2811%2F12%29+=+11+
(2) +3%2A55+-+3%2A11+=+11%2A12+
(2) +3%2A5+-+3+=+12+
(2) +15+-+3+=+12+
(2) +12+=+12+
OK
(1) +2s+%2B+2c+=+11+
(1) +2%2A%2855%2F12%29+%2B+2%2A%2811%2F12%29+=+11+
(1) +2%2A55+%2B+2%2A11+=+11%2A12+
(1) +2%2A5+%2B+2+=+12+
(1) +10+%2B+2++=+12+
(1) +12+=+12+
OK