A water tank holds 684 gallons but is leaking at a rate of 4 gallons per week. A second water tank holds 912 gallons but is leaking at a rate of 7 gallons per week. After how many weeks will the amount of water in the two tanks be the same?

76 weeks

Step-by-step explanation:

Let's write an equation for both tank. Let A be tank 1 and let B be tank 2.

So, Tank A already holds 684 galloons but is leaking at 4 galloons per week. In other words, after x weeks, the total amount of galloons Tank A holds is:

Tank B holds 912 galloons but is leaking at 7 galloons per week. So, after x weeks, the amount of galloons Tank B holds is:

To find out after how many weeks will the galloons in the two tanks be equivalent, set the two equations equal to each other and solve for x:

Add 7x to both sides. The right cancels:

Subtract 684 from both sides:

Divide both sides by 3:

So, the amount of water in the two tanks will be identical after 76 weeks.

Let's check, after 76 weeks, the amount of water left in Tank A is:

And in Tank B:

So, we're correct!

And we're done!