A hot tub holding 480 gal of water begins to empty at a rate of 5 gal/min. At the same time, an empty hot tub begins to fill at a rate of 15 gal/min. Let g represent the number of gallons of water and let t represent time in minutes. The system models this situation.

How long will it take for the hot tubs to hold equal amounts of water, and how much water will that be?

g = 480 – 5t
g = 15t

It will take
minutes for both hot tubs to hold equal amounts of water. They will each hold

gallons.

Question

A hot tub holding 480 gal of water begins to empty at a rate of 5 gal/min. At the same time, an empty hot tub begins to fill at a rate of 15 gal/min. Let g represent the number of gallons of water and let t represent time in minutes. The system models this situation.
 
How long will it take for the hot tubs to hold equal amounts of water, and how much water will that be?
 
g = 480 – 5t
g = 15t
   
It will take  
 minutes for both hot tubs to hold equal amounts of water. They will each hold

gallons.

mathmale · Answer

"Equal amounts of water" would signify that g for the first tub = g for the second tub.
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