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 minute

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Question 851865: 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,
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
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.
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let x=time it will take to fill the tub
1/270=rate at which hose can fill tub by itself
1/450=rate at which tub will empty by open drain
1/x=rate at which tub will fill with input from garden hose and drain open.
sum of individual work rates=work rate working together
1%2F270-1%2F450=1%2Fx
LCD:x(270)(450)
450x-270x=270*450
180x=121500
x=675
time it will take to fill the tub=675 min