SOLUTION: Two chemical plants are releasing toxic wastes into the atmosphere. Plant I releases a certain amount twie as fast as Plant II. Together they release that amount in 3 hours. How lo

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Question 69382: Two chemical plants are releasing toxic wastes into the atmosphere. Plant I releases a certain amount twie as fast as Plant II. Together they release that amount in 3 hours. How long does it take the slower plant to release that same amount.
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!

Let x= amount of toxic waste released
Let t= the time it takes Plant II to release x amount
Then (t/2)= the time it takes Plant I to release x amount
So Plant II releases toxic waste at the rate of x/t cu units per hour
And Plant I releases toxic waste at the rate of x/(t/2) or 2x/t cu units per hour
Now we are told that in 3 hours, Plant I and Plant II together can release the x amount of toxic waste
Sooooo
(x/t+2x/t)*3=x first, lets get rid of parens
3x/t+6x/t=x
9x/t=x divide both sides by x
9/t=1 multiply both sides by t
t=9 hours -------------------Time it takes Plant II (the slower Plant) to release x amount of toxic waste.
(t/2)=9/2=4.5 hours------------Time it takes Plant I to release x amount of waste
CK
Plant I releases at the rate of x/9
Plant II releases at the rate of x/4.5
Together they release at the rate of x/9+x/4.5. This equals:
x/9+x/4.5=x/9+2x/9=3x/9=x/3
Or in 3 hours they together have released the certain amount.

Hope this helps---ptaylor