Question

A water tank holds 1,264 gallons but is leaking at a rate of 5 gallons per week. A second water tank holds 1,580 gallons but is leaking at a rate of 9 gallons per week. After how many weeks will the amount of water in the two tanks be the same?

Answer 1

Two water tanks with different volumes and leakage rates will equalize in water volume after 79 weeks when calculated with the given initial volumes and weekly leak rates.

Step-by-step explanation:

Equalizing Water Levels in Leaking Tanks

Assuming we have two water tanks with different initial volumes and different weekly leakage rates, we want to know after how many weeks they will have the same amount of water. The first tank starts with 1,264 gallons and loses 5 gallons per week. The second tank starts with 1,580 gallons and loses 9 gallons per week.

We can set up an equation representing each tank's volume over time:

Tank 1: V1(t) = 1264 - 5t

Tank 2: V2(t) = 1580 - 9t

To find when the volumes are equal, we set V1(t) = V2(t):

1264 - 5t = 1580 - 9t

Solving this equation, we combine like terms and get:

4t = 316

Dividing both sides by 4, we find:

t = 79

So, the water levels will be equal after 79 weeks.