Question

The swimming pool is open when the high temperature is higher than 20°C (68°F) Lainey tried to swim on Monday and Thursday (which was 3 days later). The pool was open on Monday, but it was closed on Thursday. The high temperature was 30°C (86°F) on Monday, but decreased at a constant rate in the next 3 days.

Write an inequality to determine the rate of temperature decrease in degrees Celsius per day, d from Monday to Thursday.

Answer 1

To determine the rate of temperature decrease (d) from Monday to Thursday, the inequality is 20 < 30 - 3d, where 20°C is the threshold for the pool to be open.

Let T be the high temperature in degrees Celsius. The inequality to represent the rate of temperature decrease d from Monday to Thursday is:

`\[ T_{\text{Thursday}} < T_{\text{Monday}} - 3d \]`

Given that the high temperature on Monday
`(\( T_{\text{Monday}} \))` is 30°C and the pool is closed on Thursday, we know that
`\( T_{\text{Thursday}} \)` is below the threshold of 20°C:

`\[ T_{\text{Thursday}} < 20 \]`

Combine these inequalities to express the rate of temperature decrease:

`\[ 20 < 30 - 3d \]`

Lainey experienced a decline in the pool's accessibility from Monday to Thursday, with a starting temperature of 30°C. The rate of temperature decrease (d) must satisfy the inequality 20 < 30 - 3d indicating a drop below 20°C by Thursday.