SOLUTION: I am helping my daughter and this problem has us stumped. I believe the formula is t/270 t/450 = 1/t. Any help is appreciated. A garden hose can fill up a hot tub in 270 minut

Question 851855: I am helping my daughter and this problem has us stumped. I believe the formula is t/270 t/450 = 1/t. Any help is appreciated.
A garden hose can fill up a hot tub in 270 minutes, whereas the drain can empty in 450 mins. If the drain is left open how long will it take to fill the tub?
Many thanks,

Found 2 solutions by Seutip, josh_jordan:
Answer by Seutip(231) (Show Source): You can put this solution on YOUR website!
http://www.algebra.com/algebra/homework/Rational-functions/Rational-functions.faq.question.203502.html
You better watch this link. :)
Hope it'll help!
Answer by josh_jordan(263) (Show Source): You can put this solution on YOUR website!
Hello. You almost have the equation set up correctly. It should be:

This is because if the garden hose can fill up a hot tub in 270 min, in one minute, it can fill up 1/270 of the tub, and if the drain can empty in 450 minutes, in one minute, it empties 1/450 of the tub. Now, the hose and drain are working AGAINST each other, rather than WITH each other, because as the hose fills up the tub, the drain empties the tub, so you want to subtract the two instead of adding them.

Now, to solve for t, you need to multiply each fraction by the LCD, which is 1350t. Doing so will give you:

5t - 3t = 1350 ----->

2t = 1350 ----->

t = 675

So, it will take 675 minutes to fill the hot tub if the drain is open and draining the water while the garden hose is filling up the hot tub.
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