<PRE><B>Question 398138</B>
a motorboat maintained a constant speed of 12 mph relative to the water going
 23 miles upstream then returning.
 Total time for the trip was 24 hours.
 Using this information provided, what is the speed of the current in mph?
:
Let x = speed of the current
then
(12-x) = effective speed upstream
and
(12+x) = effective speed downstream
:
Write a time equation; time = dist/speed
:
time upstr + time downstr = 24 hrs
{{{23/((12-x))}}} + {{{23/((12+x))}}} = 24
:
Multiply equation by (12-x)(12+x) to get rid of the denominators, results:
23(12+x) + 23(12-x) = 24(12-x)(12+x)
:
276 + 23x + 276 - 23x = 24(144 - x^2)
:
552 = 3456 - 24x^2
:
24x^2 = 3456 - 552
:
24x^2 = 2904
divide both sides by 24
x^2 = 121
x = {{{sqrt(121)}}}
x = 11 mph is the speed of the current
;
:
That seems high, but let&#39;s check the time each way
23/(12+11) = 1.0 hr
23/(12-11) = 23 hrs
--------------------------
round trip time: 24 hrs, which confirms our solution of x = 11 mph current</PRE>