<PRE><B>Question 861850</B>
 Manny can paddle his canoe at a rate of 7 miles per hour in still water. he travels 45 miles upstream and 45 miles downstream in a total time of 14 hours. what is the speed of the current?
:
let c = rate of the current
then
(7+c) = effective speed down stream
and
(7-c) = effective speed up stream
:
Write a time equation, time = dist/speed
time down + time up = 14 hrs
{{{45/((7+c))}}} + {{{45/((7-c))}}} = 14
multiply equation by (7+c)(7-c), resulting in
45(7-c) + 45(7+c) = 14(7-c)(7+c)
315 - 45c + 315 + 45c = 14(49 - c^2)
630 = 686 - 14c^2
14c^2 = 686 - 630
14c^2 = 56
c^2 = 56/14
c^2 = 4
c = {{{sqrt(4)}}}
c = 2 km/h is the current
:
:
Check this, find the time each way
45/9 = 5
45/5 = 9
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total: 14 hrs</PRE>