SOLUTION: Len is planning a three hour trip down a river and back to his starting point. He knows he can paddle in still water at 3 miles per hour and that the rate of the current is 2 miles

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: Len is planning a three hour trip down a river and back to his starting point. He knows he can paddle in still water at 3 miles per hour and that the rate of the current is 2 miles      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 885920: Len is planning a three hour trip down a river and back to his starting point. He knows he can paddle in still water at 3 miles per hour and that the rate of the current is 2 miles per hour. How much time can he spend going downstream? How far downstream can he travel?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +d+ = the one-way distance traveled
Let +t%5B1%5D+ = time in hrs to travel downstream
Let +t%5B2%5D+ = time in hrs to travel upstream
Going downstream, Len can travel at a rate of:
+3+%2B+2+=+5+ mi/hr
Going upstream, Len can travel at a rate of:
+3+-+2+=+1+ mi/hr
------------------------
Going downstream:
(1) +d+=+5t%5B1%5D+
Going upstream:
(2) +d+=+1%2At%5B2%5D+
Also given:
(3) +t%5B1%5D+%2B+t%5B2%5D+=+3+
--------------------
From (1) and (2):
(2) +t%5B2%5D+=+5t%5B1%5D+
and
(3) +t%5B1%5D+%2B+5t%7B1%5D+=+3+
(3) ++6t%5B1%5D+=+3+
(3) +t%5B1%5D+=+.5+ hr
and
(3) +1%2F2+%2B+t%5B2%5D+=+3+
(3) +t%5B2%5D+=+2.5+ hrs
---------------------
He can spend 1/2 hr going downstream
and
(1) +d+=+5t%5B1%5D+
(1) +d+=+5%2A%281%2F2%29+
(1) +d+=+2.5+ mi
He can travel 2.5 mi downstream
--------------------------------
check:
(2) +d+=+1%2At%5B2%5D+
(2) +d+=+1%2A2.5+
(2) +d+=+2.5+ mi
OK