Question

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.

Answer 1

`160\ \text{s}`

Explanation:

The inequality that represents the situation is

`500-2.5t<100` where
`t` is the time in seconds

`\Rightarrow -2.5t<100-500`

`\Rightarrow -2.5t<-400`

`\Rightarrow 2.5t>400`

`\Rightarrow t>(400)/(2.5)`

`\Rightarrow t>160\ \text{s}`

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