Let [tex]t[/tex] be the number of minutes.
The first tank starts with 1500 liters, and loses 4 liters per minute, so after [tex]t[/tex] minutes there will be
[tex]1500-4t[/tex]
liters of water.
The second tank is filled at 6 liters per second, i.e.
[tex]6\times 60=360[/tex] liters per minute.
So, there will be
[tex]300+360t[/tex]
liters of water in the second tank after [tex]t[/tex] minutes.
The two quantities will be equal when
[tex]1500-4t=300+360t \iff 1200=364t \iff t=\dfrac{1200}{364}\approx 3.3[/tex]
so, approximately, after 3.3 minutes.
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
