SOLUTION: Hi, here's my question: Charlie rows at a constant speed downstream in the river from Amaroo to Bradden in 3 hours and back upstream in 4 hours. Assume the river flows at a cons

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: Hi, here's my question: Charlie rows at a constant speed downstream in the river from Amaroo to Bradden in 3 hours and back upstream in 4 hours. Assume the river flows at a cons      Log On

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Question 982496: Hi, here's my question:
Charlie rows at a constant speed downstream in the river from Amaroo to Bradden in 3 hours and back upstream in 4 hours. Assume the river flows at a constant rate. Find the number of hours it would take a piece of driftwood to float downstream from Amaroo to Bradden.
Thank you so so much for your help! :D
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Charlie has a speed due to his rowing and the current,
but the driftwood only has speed due to the current
Let +s+ = Charlie's speed without the current
Let +c+ = the speed of the current
+s+%2B+c+ = Charlie's speed going downstream
+s+-+c+ = charlie's speed going upstream
Let +d+ = distance from Amaroo to Bradden in km
----------------------------------------------
Equation for going downstream:
(1) +d+=+%28+s+%2B+c+%29%2A3+
Equation for going upstream:
(2) +d+=+%28+s+-+c+%29%2A4+
----------------------------
Plug (1) into (2)
(3) +%28+s+%2B+c+%29%2A3+=+%28+s+-+c+%29%2A4+
+3s+%2B+3c+=+4s+-+4c+
+s+=+7c+
--------------
Add (1) and (2)
+2d+=+7s+-+c+
+2d+=+7%2A7c+-+c+
+2d+=+48c+
+d+=+c%2A%28+24+%29+
--------------------
It takes 24 hrs for the driftwood to float downstream
check:
(1) +d+=+%28+s+%2B+c+%29%2A3+
(1) +d+=+%28+s+%2B+d%2F24+%29%2A3+
(1) +d+=+3s+%2B+d%2F8+
(1) +%287%2F8%29%2Ad+=+3s+
(1) +d+=+s%2A%2824%2F7%29+
and
(2) +d+=+%28+s+-+d%2F24+%29%2A4+
(2) +d+=+4s+-+d%2F6+
(2) +%287%2F6%29%2Ad+=+4s+
(2) +d+=+%286%2F7%29%2A4s+
(2) +d+=+s%2A%2824%2F7%29+
OK
Hope I got it!