The air conditioner in Mr. Blakely’s office can cool the room by 10 degrees in 90 minutes. Two doors down, Mr. Burch has an office of the same size but a more efficient air conditioner, which can cool the room by 10 degrees in 60 minutes. If both air conditioners are attached to Mr. Blakely’s office, how long would it take to cool the room by 10 degrees?

When combining the cooling rates of both Mr. Blakely's and Mr. Burch's air conditioners, it would take 36 minutes to cool Mr. Blakely's office by 10 degrees.

Explanation:

The time needed to cool Mr. Blakely's office by 10 degrees using both air conditioners can be found by first determining the individual cooling rates of each air conditioner, then combining them for joint operation. Mr. Blakely's air conditioner cools the room by 10 degrees in 90 minutes, which is equivalent to a rate of 1/9 degrees per minute. Mr. Burch's air conditioner cools the room by the same 10 degrees in 60 minutes, equal to a rate of 1/6 degrees per minute.

When operating simultaneously, the total cooling rate is the sum of the individual rates: (1/9 + 1/6) degrees per minute, which simplifies to (2/18 + 3/18) or 5/18 degrees per minute. To cool the room by 10 degrees, we divide the target change in temperature by the combined rate: 10 / (5/18) minutes = 36 minutes. Therefore, it would take both air conditioners 36 minutes to cool Mr. Blakely's office by 10 degrees.

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Talanat Talanat · Answer 2 · 2024-10-11T08:31:24-04:00

Answer:

it will take 45 minutes to cool the room 10 degrees if we attach both air conditioners to Mr. Blakely's office.

Step-by-step explanation:

If we attach both air conditioners to Mr. Blakely's office, the combined cooling rate will be 10 degrees / 90 min + 10 degrees / 60 min = 20 degrees / 90 min = 2 degrees / 9 min.

To cool the room 10 degrees, it will take 10 degrees / 2 degrees/9 min = 5 * 9 min = 45 min.