SOLUTION: please help me solve this word problem: two pipes working together drain a water holding tank in 6 hours. if used alone to empty the tank, one takes 2 hours longer than the other.
Question 273955: please help me solve this word problem: two pipes working together drain a water holding tank in 6 hours. if used alone to empty the tank, one takes 2 hours longer than the other. how long does each take to empty the tank if used alone? Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! two pipes working together drain a water holding tank in 6 hours.
if used alone to empty the tank, one takes 2 hours longer than the other.
how long does each take to empty the tank if used alone?
:
Let x = time for one pipe to drain it by itself
then
(x+2) = time for the other pipe to by itself
;
Let the completed job = 1, (a drained tank)
:
Each pipe does a fraction of the job, the two fractions add up to one. + = 1
Multiply equation by x(x+2), results:
6(x+2) + 6x = x(x+2)
;
6x + 12 + 6x = x^2 + 2x
:
12x + 12 = x^2 + 2x
Arrange as a quadratic equation
0 = x^2 + 2x - 12x - 12
:
x^2 - 10x - 12 = 0
We have to use the quadratic formula to solve this:
In this equation a=1; b=-10; c=-12
:
We only want the positive solution
x =
x = 11.08 hrs, for the 1st pipe to drain it alone
and
11.08 + 2 = 13.08 hrs for the 2nd pipe alone
;
:
Check solution
6/11.08 + 6/13.08 =
.54 + .46 = 1; confirms our solutions
