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Water is pumped out of a 500-gallon tank at a rate of 2.5 gallons per second. The inequality 500−2.5t<100 can be used to determine the time t in seconds, after which there will be less than 100 gallons of water remaining in the tank.

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Answer:

[tex]160\ \text{s}[/tex]

Step-by-step explanation:

The inequality that represents the situation is

[tex]500-2.5t<100[/tex] where [tex]t[/tex] is the time in seconds

[tex]\Rightarrow -2.5t<100-500[/tex]

[tex]\Rightarrow -2.5t<-400[/tex]

[tex]\Rightarrow 2.5t>400[/tex]

[tex]\Rightarrow t>\dfrac{400}{2.5}[/tex]

[tex]\Rightarrow t>160\ \text{s}[/tex]

So, the time after which there will be less than 100 gallons of water is [tex]160\ \text{s}[/tex].

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