Question

From an oil tank, oil is being drained at a constant linear rate. Four hours after draining of the tank began, the volume of oil in the tank was $740$ gallons, and seven hours after draining of the tank began, the volume was $545$ gallons. Which of the following functions best models $v\left(t\right)$, the volume of oil in the tank, in gallons, $t$ hours after draining of the tank began?

• A. $v\left(t\right)=740-t$
• B. $v\left(t\right)=740-65t$
• C. $v\left(t\right)=1000-195t$
• D. $v\left(t\right)=1000-65t$

Answer 1

Answer: (D)

$v\left(t\right)=1000-65t$

Given that volume of oil tank after draining of tank $4$ hours is $740$ gallons

And after $7$ hours draining of tank the volume is $545$ gallons.

Then in $7-4$ hour oil draining the volume $=740-545=195$ gallon.

Then in $1$ hour oil draining the volume $=$ $\frac{195}{3}=65$ gallon.

Then in $t$ hour oil draining the volume $=65t$ gallon.

And in $4$ hour oil draining the volume at before $=$ $65\times 4=260$ gallon.

So on stating time the volume of oil in tank $=740+260=1000$ gallon.

Then volume of oil in tank after tank $v\left(t\right)=1000-65t$.

So $v\left(t\right)=1000-65t$ is write answer