Laura is a chemist working with liquids and solutions. She has two large cylindrical barrels that can hold up to 2,000 liters each. The first barrel contains 900 liters of solution, and the second barrel contains 100 liters of solution. Laura begins draining the first barrel at a rate of 36 liters per minute at the same time she begins filling the second barrel. Laura fills the second barrel with 44 liters of solution every minute.

Which inequality represents the seconds, $ s $, when the second barrel contains a greater or equal amount of solution than the first barrel?

We know that the first barrel starts with 900 liters and is drained at a rate of 36 liters per minute, and the second barrel starts with 100 liters and is being filled at 44 liters per minute.

To find the time when the second barrel will contain an equal or greater amount of solution than the first barrel, we must set up an inequality where the amount of solution in the second barrel is greater than or equal to the amount in the first barrel. We convert the rates to liters per second (since we are asked for the time in seconds) and set up the inequality using these rates:

36 liters per minute = 0.6 liters per second (since 36 liters / 60 seconds = 0.6 liters/sec)
44 liters per minute = 0.7333... liters per second (since 44 liters / 60 seconds
approximately 0.7333 liters/sec)

We use these rates to create the inequality:

100 + 0.7333s ≥ 900 - 0.6s

Where s is the number of seconds. Solving this inequality for s tells us the time when the second barrel has as much or more solution than the first barrel.