Question

If `V=1.5*t+0.0080*t^2` has the units millions of cubic feet per month, how would you rewrite the equation if you wanted the result in cubic feet per second?

Answer 1

`V=3.888*t + 5,374.8*t^2`

Explanation:

The volume, `V`, is given as `10^6` cubic feet. Converting this to just cubic feet requires us to divide `V` by a factor of `10^6`.

Converting months to seconds requires several multiplying factors

`(30 cancel(" days"))/(1 " month")xx(24 cancel(" hours"))/(1 cancel(" day"))xx(60 cancel(" min"))/(1 cancel(" hour"))xx(60 " sec")/(1 cancel(" min"))`
`=2.592xx10^6 "sec"/"month"`

Multiplying the volume, `V`, and time, `t` by these factors gives

`V/10^6=2.592xx10^6*1.5*t+(2.592xx10^6)^2*0.008*t^2`

`V=10^-6(2.592xx10^6*1.5*t+(2.592xx10^6)^2*0.008*t^2)`
`V=2.592*1.5*t+10^-6*(2.592xx10^6)^2*0.008*t^2`
`V=2.592*1.5*t+(2.592)^2*0.008xx10^6t^2`
`V=3.888*t + 5,374.8*t^2`