The swimming pool is open when the high temperature is higher than . Lainey tried to swim on Monday and Thursday (which was days later). The pool was open on Monday, but it was closed on Thursday. The high temperature was on Monday, but decreased at a constant rate in the next days.Write an inequality to determine the rate of temperature decrease in degrees Celsius per day, , from Monday to Thursday.
Question
The swimming pool is open when the high temperature is higher than . Lainey tried to swim on Monday and Thursday (which was days later). The pool was open on Monday, but it was closed on Thursday. The high temperature was on Monday, but decreased at a constant rate in the next days.Write an inequality to determine the rate of temperature decrease in degrees Celsius per day, , from Monday to Thursday.
Solution
The problem seems to be missing some key information such as the high temperature threshold for the pool to be open, the high temperature on Monday, and the number of days between Monday and Thursday. However, I can still explain how to set up the inequality once you have that information.
Let's denote:
- T as the high temperature on Monday,
- t as the threshold temperature for the pool to be open,
- d as the number of days between Monday and Thursday,
- r as the rate of temperature decrease in degrees Celsius per day.
Since the pool was open on Monday but closed on Thursday, the temperature on Thursday must have been less than the threshold temperature t. If the temperature decreased at a constant rate r from Monday to Thursday, we can express the temperature on Thursday as T - r*d.
The fact that the pool was closed on Thursday gives us the inequality:
T - r*d < t
This inequality can be used to determine the rate of temperature decrease r once you know the values of T, t, and d.
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