SOLUTION: Allison can row a boat 1 mile upstream (against the current) in 24 minutes. She can row the same distance downstream in 13 minutes. Assume that both the rowing speed and the speed

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Question 801939: Allison can row a boat 1 mile upstream (against the current) in 24 minutes. She can row the same distance downstream in 13 minutes. Assume that both the rowing speed and the speed of the current are constant.
Find the speed at which Allison is rowing and the speed of the current.
Found 2 solutions by richwmiller, josmiceli:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
r*t=d
(r-c)*24/60=1,
(r+c)*13/60=1
c = 55/52, r = 185/52
c=1.0577, r=3.5577

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = Allison's speed rowing in still water
Let +c+ = the speed of the current
+s+-+c+ = her speed rowing against the current
+s+%2B+c+ = her speed rowing with the current
------------------
Equation for rowing against the current:
(1) +1+=+%28+s+-+c+%29%2A%2824%2F60%29+
Equation for rowing with the current:
(2) +1+=+%28+s+%2B+c+%29%2A%2813%2F60%29+
--------------------------
(1) +60+=+24s+-+24c+
(1) +6s+-+6c+=+15+
and
(2) +13s+%2B+13c+=+60+
---------------------
Multiply both sides of (1) by +13%2F6+
and add (1) and (2)
(2) +13s+%2B+13c+=+60+
(1) +13s+-+13c+=+32.5+
------------------------
+26s+=+92.5+
+s+=+3.558+ mi/hr
and, since
(1) +6s+-+6c+=+15+
(1) +6%2A3.558+-+6c+=+15+
(1) +21.348+-+15+=+6c+
(1) +6c+=+6.348+
(1) +c+=+1.058+
----------------
Allison's speed rowing in still water is 3,558 mi/hr
The speed of the current is 1.058 mi/hr