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A water tank currently has 130 gallons of water and is being filled by 10 gallons every hour. A second water tank currently has 280 gallons of water and is being drained by 5 gallons every hour. After how many hours will the two tanks have the same amount of water? Show your equations

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Answer: let the hours they both have equal amount of water be X

130+10x=280-5x

10x+5x=280-130

15x=150

x=10hrs

Step-by-step explanation:

Answer:

After 10 hours, both tanks would have the same amount of water.

Step-by-step explanation:

The first tank has 130 gallons already, that's its initial condition, and it's being filled by 10 gallons every hour. This can be modeled by the following equation

[tex]T_{1}=130+10x[/tex]

Where [tex]x[/tex] represents hours.

The second tank has 280 gallons of water, that's its initial condition, and it's being drained by 5 gallons every hour. In this case, "drained" refers to a negative variation

[tex]T_{2}= 280-5x[/tex].

Now, we need to make them equal, because we need to find how many hours will take to have the same amount of water. So,

[tex]T_{1} =T_{2}\\ 130+10x=280-5x\\10x+5x=280-130\\15x=150\\x=\frac{150}{15}\\x=10[/tex]

Therefore, after 10 hours, both tanks would have the same amount of water.

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