Question

A water tank has 1,500 liters of water. It has a leak, losing 4 liters per minute. At the same time, a second tank has 300 liters and is being filled at a rate of 6 liters per second. Make a system of equations. After how many minutes will they have a same amount of water in the tank?

Answer 1

Let $t$ be the number of minutes.

The first tank starts with 1500 liters, and loses 4 liters per minute, so after $t$ minutes there will be

$1500-4t$

liters of water.

The second tank is filled at 6 liters per second, i.e.

$6\times 60=360$ liters per minute.

So, there will be

$300+360t$

liters of water in the second tank after $t$ minutes.

The two quantities will be equal when

$1500-4t=300+360t \iff 1200=364t \iff t=\dfrac{1200}{364}\approx 3.3$

so, approximately, after 3.3 minutes.

Answer 2

Answer: it will take about 3.3 minutes for both tanks to have the same amount of water.

Step-by-step explanation:

Let x represent the number of minutes it will take both tanks to have same amount of water.

A water tank has 1,500 liters of water. It has a leak, losing 4 liters per minute. This means that in x minutes, the volume of water in the tank would be

1500 - 4x

At the same time, a second tank has 300 liters and is being filled at a rate of 6 liters per second. Converting 6 liters per second to minutes, it becomes 60 × 6 = 360 liters per minute. This means that in x minutes, the volume of water in the tank would be

300 + 360x

For both tanks to have same amount of water, then

1500 - 4x = 300 + 360x

360x + 4x = 1500 - 300

364x = 1200

x = 1200/364 = 3.3 minutes