<PRE><B>Question 316542</B>
a motor boat maintained speed of 27 miles per hour relative to the water going 20 miles upstream and returning.
 The total time of the trip was 1.5 hours. What is the speed of the current?
:
Let c = speed of the current
then
(27-c) = effective speed upstream
and
(27+c) = effective speed downstream
:
Write a time equation; time = dist/speed
:
Time up + time down = 1.5 hrs
{{{20/(27-c)}}} + {{{20/(27+c)}}} = 1.5
Multiply equation by (27-c)(27+c), results
20(27+c) + 20(27-c) = 1.5(27-c)(27+c)
:
540 + 20c + 540 - 20c = 1.5(729-c^2)
:
1080 = 1093.5 - 1.5c^2
:
1.5c^2 = 1093.5 - 1080
:
1.5c^2 = 13.5
c^2 = {{{13.5/1.5}}}
c^2 = 9
c = {{{sqrt(9)}}}
c = 3 mph is the speed of the current
:
:
See if that&#39;s true, find the time of each
20/30 = .67
20/24 = .83
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totals:1.5 hrs</PRE>