SOLUTION: I need to solve this word problem in the form of a quadratic equation and am having difficulty. Please help me. Rita rows 12 km upstream and 12 km downstream in 3 hours. The speed

Algebra ->  Algebra  -> Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: I need to solve this word problem in the form of a quadratic equation and am having difficulty. Please help me. Rita rows 12 km upstream and 12 km downstream in 3 hours. The speed      Log On

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Question 84762: I need to solve this word problem in the form of a quadratic equation and am having difficulty. Please help me.
Rita rows 12 km upstream and 12 km downstream in 3 hours. The speed of her boat in still water is 9 km/hr. Find the speed of the stream.

Answer by dolly(163) About Me  (Show Source):
You can put this solution on YOUR website!

Let the speed of the stream = 'x' km/hr
speed of the boat = 9km/hr
Relative Speed upstream = (9-x) km/hr
Relative speed downstream = (9+x) km/hr
Distance travelled = 12 km up and 12 km down
Time taken for upward journey = distance/speed
= 12/(9-x) hrs
Time taken for downward journey = distance/speed
= 12/(9+x) hrs
Total time taken given to be = 3 hrs

==> 12/9-x + 12/9+x = 3
==> 12(9+x) + 12(9-x) = 3(9+x)(9-x)
==> 108 + 12x + 108 - 12x = 3(81 - x^2)[as (a+b)(a-b) = a^2-b^2)]
==> 216 = 243 - 3x^2
==> 3x^2 = 243 - 216
==> 3x^2 = 27
==> x^2 = 27/3
= 9
==> x = 3
Thus the speed of the boat = 3 km/hr
Good Luck!!!