gabbyalicorn
  • gabbyalicorn
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. @foxymangle
Mathematics
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SOLVED
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katieb
  • katieb
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gabbyalicorn
  • gabbyalicorn
@FOXYXMANGLE
563blackghost
  • 563blackghost
We would do this.... \[480-5t=15t\] we would get t by itself to get the equal amounts
gabbyalicorn
  • gabbyalicorn
so 480-5t-5t=15t-5t?

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gabbyalicorn
  • gabbyalicorn
Did I do this correctly?
563blackghost
  • 563blackghost
The process would actually start with adding 5t to get 5t to the other side of the equation and to cancel it out....|dw:1449517228516:dw|
gabbyalicorn
  • gabbyalicorn
What would we do with 480=20+?
563blackghost
  • 563blackghost
We then would divide 20t by 20 to cancel 20 so what we do to one side we do to the other so we would also divide 480 by 20...\[\frac{ 480 }{ 20 } = \frac{ 20t }{ 20 }\]
gabbyalicorn
  • gabbyalicorn
Which would be 24?
563blackghost
  • 563blackghost
Correct! It would be 24 xD
gabbyalicorn
  • gabbyalicorn
Just 24? So it will take 24 minutes, but what about the amount of gallons?
563blackghost
  • 563blackghost
Yup it would take 24min.... Now to get the gallons of each we would input 24 where t is and do the equation soo.... \[g = 480 - 5(24)\] and \[g = 15(24)\]
gabbyalicorn
  • gabbyalicorn
okay, for g its 360
gabbyalicorn
  • gabbyalicorn
Am I right?
563blackghost
  • 563blackghost
Correct! So each will take 24 minute and will hold 360 gallons...
gabbyalicorn
  • gabbyalicorn
Oh wow! ^///^ Thank you so much!!! I really appreciate it.
563blackghost
  • 563blackghost
Np ^^ Glad I was of help! If you ever need help in the future just tag me in your question and I'll try to help as much as I can xD
gabbyalicorn
  • gabbyalicorn
Okay, thanks. :)

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