Answer the following questions based on the information given below.
The air-conditioner (AC) in a large room can be operated either in REGULAR mode or in POWER mode to reduce the temperature.
If the AC operates in REGULAR mode, then it brings down the temperature inside the room (called inside temperature) at a constant rate to the set temperature in 1 hour. If it operates in POWER mode, then this is achieved in 30 minutes.
If the AC is switched off, then the inside temperature rises at a constant rate so as to reach the temperature outside at the time of switching off in 1 hour.
The temperature outside has been falling at a constant rate from 7 pm onward until 3 am on a particular night. The following graph shows the inside temperature between 11 pm (23:00) and 2 am (2:00) that night.
The following facts are known about the AC operation that night.
• The AC was turned on for the first time that night at 11 pm (23:00).
• The AC setting was changed (including turning it on/off, and/or setting different temperatures) only at the beginning of the hour or at 30 minutes after the hour.
• The AC was used in POWER mode for longer duration than in REGULAR mode during this 3-hour period.
Q6
LR - Scheduling & Processes TYPE IN THE ANSWER
What was the temperature outside, in degree Celsius, at 1 am?
Rising segments mean the AC is off. When off, the room rises at a rate that would reach the outside temperature in 1 hour.
0:00–0:30: it rises 5° in half an hour, so the gap was 10°. Outside at 0:00 = 26 + 10 = 36.
1:00–1:30: it rises 4° in half an hour, so the gap was 8°. Outside at 1:00 = 26 + 8 = 34.
So the outside temperature falls 2° per hour. It was 38 at 23:00, 42 at 21:00 and 32 at 2:00.
Falling segments:
23:00–0:00 (38 → 26, 12° per hour): either REGULAR set to 26 for the full hour, or POWER set to 32 (23:00–23:30) followed by POWER set to 26 (23:30–0:00).
0:30–1:00 (31 → 26): POWER set to 26, or REGULAR set to 21 and switched off at 1:00.
1:30–2:00 (30 → 28): POWER set to 28, or REGULAR set to 26.
Power must run longer than Regular. If the first hour were REGULAR, POWER could total at most 0.5 + 0.5 = 1 hour, which is not longer. So the first hour is POWER at 32, then POWER at 26, with a setting change at 23:30.
From the 1:00–1:30 rise of 4° in half an hour, outside at 1:00 = 26 + 8 = 34 °C.
