SOLUTION: word problem associated with quadratic equation chapter:: a motorboat maintained a constant speed of 12 mph relative to the water going 23 miles upstream then returning. Total

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Question 398138: word problem associated with quadratic equation chapter::
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?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
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%2F%28%2812-x%29%29 + 23%2F%28%2812%2Bx%29%29 = 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%28121%29
x = 11 mph is the speed of the current
;
:
That seems high, but let'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