SOLUTION: A woman rows a boat upstream from one point on a river to another point 9km away in 1 hour. The return trip with the current takes only 50 minutes. How fast would she be rowing

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Question 852908: A woman rows a boat upstream from one point on a river to another point 9km away in 1
hour. The return trip with the current takes only 50 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 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 upstream:
(1) +9+=+%28+s+-+c+%29%2A1+
Equation for rowing downstream:
(2) +9+=+%28+s+%2B+c+%29%2A%28+50%2F60+%29+
------------------------------
Add the equations:
(1) +s+-+c+=+9+
(2) +s+%2B+c+=+9%2A%286%2F5%29+
---------------------
+2s+=+9+%2B+54%2F5+
+2s+=+45%2F5+%2B+54%2F5+
+2s+=+99%2F5+
+s+=+9.9+
and
(1) +s+-+c+=+9+
(1) +9.9+-+c+=+9+
(1) +c+=+.9+
-----------------
Her speed rowing in still water is 9.9 km/hr
The speed of the current is .9 km/hr
check:
(2) +9+=+%28+s+%2B+c+%29%2A%28+5%2F6+%29+
(2) +9+=+%28+9.9+%2B+.9+%29%2A%28+5%2F6+%29+
(2) +9+=+10.8%2A%285%2F6%29+
(2) +9+=+9+
OK