Question

A scientist is conducting an experiment with liquids. Liquid A cannot cool more than 18°C or it will turn into a solid. The scientist begins to cool the liquid at a constant rate of 3°C per hour. Write an inequality to represent t, the number of hours the scientist can cool Liquid A without changing its state of matter.

(a) t ≤ 6
(b) t ≥ 6
(c) t < 6
(d) t > 6

Answer 1

To represent the time t the scientist can cool Liquid A without it turning solid, we establish the inequality 3°C * t ≤ 18°C, which simplifies to (a) t ≤ 6.

Step-by-step explanation:

The question asks us to write an inequality to represent t, the number of hours the scientist can cool Liquid A without changing its state of matter, given that the liquid cannot cool more than 18°C or it will turn into a solid, and it is being cooled at a constant rate of 3°C per hour. Since cooling happens at 3°C per hour, if we let t be the number of hours, the total decrease in temperature after t hours would be 3°C times t, which we do not want to exceed 18°C. This can be translated into the inequality 3°C * t ≤ 18°C. When we solve for t, we divide both sides by 3°C, leading to t ≤ 6. Therefore, the correct inequality is (a) t ≤ 6.