Question

Hotel Management: The Airgle AG800 can purify the air in a conference hall in 20 fewer minutes than it takes the Airgle AG950 to do the same job. Together, the two machines can purify the air in the conference hall in 10.5 min. How long would it take each machine, working alone, to purify the air in the room?

Answer 1

Let x be the time for the AG800. Then the time for the AG950 is x + 20.
$\frac{1}{x}+\frac{1}{x+20}=\frac{2}{21}$
$\frac{x+20+x}{x(x+20)}=\frac{2}{21}$
Cross-multiplying and simplifying, we get:
$2x^{2}-2x-420=0$
The positive solution to this quadratic is: x = 15.
The answer is: Time for model AG800 = 15 minutes: time for model AG950 = 35 minutes.