Question

It is currently 0°C outside. The temperature is dropping 2.5°C every hour. Identify an inequality that represents the number of hours that must pass for the temperature to drop below -20c.

Answer 1

To determine when the temperature will be below -20°C, we set up the inequality 0°C - 2.5°C × h < -20°C and solve for 'h', which is the number of hours. After subtracting the initial temperature and dividing by the rate of change, we get h > 8, meaning that it will take more than 8 hours for the temperature to drop below -20°C.

Step-by-step explanation:

To determine the inequality that represents the number of hours that must pass for the temperature to drop below -20°C, we will set up an inequality with the initial temperature and the rate of change. The temperature starts at 0°C and drops by 2.5°C every hour. We want to find the number of hours, which we will call 'h', for when the temperature is less than -20°C.

The inequality is:

0°C - 2.5°C × h < -20°C

To solve this inequality for 'h', we follow these steps:

1. Subtract 0°C from both sides of the inequality:
2. - 2.5°C × h < -20°C
3. Divide both sides by -2.5°C to solve for 'h' (recall that dividing by a negative number reverses the inequality direction):
4. h > -20°C / -2.5°C
5. Calculate the result:
6. h > 8

The number of hours that must pass for the temperature to drop below -20°C is greater than 8 hours.