Question

A water tank holds 276 gallons but is leaking at a rate of 3 gallons per week. A second water tank holds414 gallons but is leaking at a rate of 5 gallons per week. After how many weeks will the amount of waterin the two tanks be the same?The amount of water in the two tanks will be the same inweeks.

Answer 1

In order to solve the problem we will first create equations to represent the volume of water on the gallons through the weeks. The output of the functions will be the volume of each and the entry will be the number of weeks passed.

For the first one:

`\text{vol(week) = 276 -3}\cdot week`

While on the second one:

`\text{vol(week) = 414 -5}\cdot week`

In order to calculate the number of weeks it'll take until they have the same volume of water we need to find the "week" which would make them equal. So we will equate both expressions and solve for that variable.

`\begin{gathered} 276\text{ - 3}\cdot week\text{ = 414 - 5}\cdot week \\ 5\cdot\text{week - 3}\cdot week\text{ = 414 - 276} \\ 2\cdot\text{week = }138 \\ \text{week = }(138)/(2)\text{ = }69 \end{gathered}`

It'll take 69 weeks for the tanks to have the same volume.