Question

The Honeywell HQ17 air cleaner takes twice as long as the EV25 to clean the samevolume of air. Together the two machines can clean the air in a 25-ft by 24-ft banquetroom in 10 minutes. How long would it take each machine working alone to clean the airin the room?

Answer 1

The Honeywell EV25 air cleaner requires 3.33 minutes, while the HQ17 takes 6.67 minutes to independently purify the air in the banquet room. Together, they achieve the task in 10 minutes.

Let x represent the time taken by the Honeywell EV25 air cleaner, and 2x denote the time taken by the Honeywell HQ17 air cleaner, as it takes twice as long. Combined, these machines can purify the air in a 25-ft by 24-ft banquet room in 10 minutes.

The equation expressing their joint efficiency is x + 2x = 3x, representing the combined rate of air purification. Setting this equal to 10 minutes, we find that x = 3.33 minutes, the time taken by the EV25 alone. Consequently, the HQ17, taking twice as long, would require 2 * 3.33 = 6.67 minutes to complete the task individually.

The Honeywell EV25 air cleaner alone needs 3.33 minutes, while the Honeywell HQ17 air cleaner requires 6.67 minutes to independently purify the air in the specified banquet room.

Answer 2

Given:

The Honeywell HQ17 air cleaner takes twice as long as the EV25 to clean the same

volume of air.

Let, x be the time taken by Honeywell EV25 air cleaner.

And 2x be the time taken by Honeywell HQ17 air cleaner.

Together the two machines can clean the air in 10 min.

`\begin{gathered} x+2x=10 \\ 3x=10 \\ x=(10)/(3)=3.33\text{ min} \end{gathered}`

So, time takes by Honeywell HQ17 air cleaner is,

`2x=2((10)/(3))=6.67\text{ min}`

Answer:

The time taken by Honeywell EV25 air cleaner is 3.33 min.

The time taken by Honeywell HQ17 air cleaner is 6.67 min.