SOLUTION: a garden hose takes 180 minutes to fill up a hot tub, whereas it takes 300 minutes to drain it, if the drain is accidentally left open how long will it take to fill the hot tub?

Question 960284: a garden hose takes 180 minutes to fill up a hot tub, whereas it takes 300 minutes to drain it, if the drain is accidentally left open how long will it take to fill the hot tub?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
rate of filling is 1/180 of the tub in one minute.
rate of emptying is 1/300 of the tub in one minute.

rate * time = quantity.
quantity is 1 full tub.
rate of filling and emptying work against each other, so their rates are subtractive.
time is what you want to find.

equation becomes:

(1/180 - 1/300) * T = 1
multiply both sides of this equation by 180 * 300 and you get:

(300 - 180) * T = 180 * 300

simplify to get:

120 * T = 180 * 300

divide both sides of this equation by 120 to get:

T = 180 * 300 / 120

simplify to get:

T = 450 minutes.

in 450 minutes, 450/180 = 2.5 times the tub has been filled and 450 / 300 = 1.5 times the tub has been emptied resulting in 1 full tub.

every minute 1/180 of the tub is being filled and 1/300 of the tub is being empties, result in a net fill of 1/450 of the tub being filled.

at that rate, the tub will be filled in 450 minutes.

the solution checks out.

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