SOLUTION: In a river with a steady current, it takes Mary 6 minutes to swim upstream a certain distance, but only 3 minutes for her to swim back. Suppose, instead, she swam upstream the same

Algebra ->  Equations -> SOLUTION: In a river with a steady current, it takes Mary 6 minutes to swim upstream a certain distance, but only 3 minutes for her to swim back. Suppose, instead, she swam upstream the same      Log On


   

Question 1065431: In a river with a steady current, it takes Mary 6 minutes to swim upstream a certain distance, but only 3 minutes for her to swim back. Suppose, instead, she swam upstream the same distance as before but floated, not swam, back to her starting point. How long does this round trip take?
Found 2 solutions by josmiceli, ikleyn:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
there is no information about the distance, so
I will call it +1+ unit of distance ( miles or whatever )
------------------------
Let +s+ = Mary's speed swimming in still water
Let +c+ = the speed of the current
Going upstream:
(1) +1+=+%28+s+-+c+%29%2A6+
(1) +s+-+c+=+1%2F6+
Going downstream:
(2) +1+=+%28+s+%2B+c+%29%2A+3+
(2) +s+%2B+c+=+1%2F3+
------------------------
Note that the rates are in units / min
Add (1) and (2)
(1) +s+-+c+=+1%2F6+
(2) +s+%2B+c+=+1%2F3+
----------------------
+2s+=+1%2F6+%2B+2%2F6+
+2s+=+1%2F2+
+s+=+1%2F4+
and
(2) +s+%2B+c+=+1%2F3+
(2) +1%2F4+%2B+c+=+1%2F3+
(2) +c+=+4%2F12+-+3%2F12+
(2) +c+=+1%2F12+
------------------------------------
Let +t%5B1%5D+ = time in minutes to swim
upstream 1 unit of distance
Let +t%5B2%5D+ = time in minutes to float
downstream 1 unit of distance
-------------------------------------
Swimming upstream:
(3) +1+=+%28+1%2F4+-+1%2F12+%29%2At%5B1%5D+
(3) +1+=+%28+1%2F6+%29%2At%5B1%5D+
(3) +t%5B1%5D+=+6+ min
Floating downstream:
(4) +1+=+%281%2F12%29%2At%5B2%5D+
(4) +t%5B2%5D+=+12+
-----------------------
+t%5B1%5D+%2B+t%5B2%5D+=+6+%2B+12+
+t%5B1%5D+%2B+t%5B2%5D+=+18+
The round trip takes 18 min
----------------------------
Check the math, and get another
opinion if needed

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
I checked it.

Everything is correct.

The solution and the answer are correct.

There is similar problem, solved in the lesson
    - Unpowered raft floating downstream along a river
in this site.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lesson is the part of this textbook under the topic "Travel and distance".