Question

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

Answer 1

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

Explanation:

Answer 2

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

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

`T_(1)=130+10x`

Where
`x` 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

`T_(2)= 280-5x`.

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,

`T_(1) =T_(2)\\ 130+10x=280-5x\\10x+5x=280-130\\15x=150\\x=(150)/(15)\\x=10`

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