SOLUTION: I need help setting up and answering this problem: The speed of the current in a river is 2mph. John rows 13 miles upstream and the same 13 miles back downstream. If the trip down

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Question 921813: I need help setting up and answering this problem:
The speed of the current in a river is 2mph. John rows 13 miles upstream and the same 13 miles back downstream. If the trip downstream took 2 hours less than the trip upstream, what was John's rowing speed?
Found 2 solutions by josgarithmetic, josmiceli:
Answer by josgarithmetic(39628) About Me  (Show Source):
You can put this solution on YOUR website!
r, rowing speed if no current
RT=D is uniform rates travel rule.
Using multiplicative inverse of R, T=D/R.

_______________________rate__________time___________distance
UPSTREAM_______________r-2___________13%2F%28r-2%29___________13
DOWNSTRM_______________r+2___________13%2F%28r%2B2%29__________13


The description indicates that highlight%2813%2F%28r-2%29-13%2F%28r%2B2%29=2%29.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = the speed rowing in still water in mi/hr
+s+-+2+ = his speed rowing upstream in mi/hr
+s+%2B+2+ = his speed rowing downstream in mi/hr
Let +t+ = time in hrs to row upstream
+t+-+2+ = time in hrs to row downstream
---------------------------------------
Equation for rowing upstream:
(1) +13+=+%28+s-2+%29%2At+
Equation for rowing downstream:
(2) +13+=+%28+s%2B2+%29%2A%28+t-2+%29+
--------------------------
(2) +13+=+t%2A%28+s%2B2+%29+-+2s+-+4+
and
(1) +t+=+13+%2F+%28+s-2+%29+
Substitute (1) into (2)
(2) +17+=+%28+13%2F%28+s-2%29+%29%2A%28+s%2B2+%29+-+2s++
(2) +17%2A%28+s-2+%29+=+13%2A%28+s%2B2+%29+-+2s%2A%28+s-2+%29+
(2) +17s+-+34+=+13s+%2B+26+-+2s%5E2+%2B+4s+
(2) +2s%5E2+%2B+17s+-+13s+-+4s+=+34+%2B+26+
(2) +2s%5E2+=+60+
(2) +s%5E2+=+30+
(2) +s+=+5.477+
John's rowing speed is 5.477 mi/hr
-----------
check:
(1) +13+=+%28+s-2+%29%2At+
(1) +13+=+%28+5.477-2+%29%2At+
(1) +13+=+3.477t+
(1) +t+=+3.739+
and
(2) +13+=+%28+s%2B2+%29%2A%28+t-2+%29+
(2) +13+=+%28+5.477%2B2+%29%2A%28+3.739-2+%29+
(2) +13+=+7.477%2A1.739+
(2) +13+=+13.003+
Error due to rounding off, I think
Check all my math