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A chemical lab is scheduled to go through two air ventillation systems, a basic system and a more advanced system that takes half an hour and two hours respectively to fully ventillate the room. If both ventillation systems were to operate at the same time with thier respective constant rates, how many hours would it take to fully ventilate the chemical lab?
(A) 1/4
(B) 1/3
(C) 2/5
(D) 5/4
(E) 3/2
(A) 1/4
(B) 1/3
(C) 2/5
(D) 5/4
(E) 3/2
10 Sep 2013, 18:30
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amgelcer
A chemical lab is scheduled to go through two air ventillation systems, a basic system and a more advanced system that takes half an hour and two hours respectively to fully ventillate the room. If both ventillation systems were to operate at the same time with their respective constant rates, how many hours would it take to fully ventilate the chemical lab?
(A) 1/4
(B) 1/3
(C) 2/5
(D) 5/4
(E) 3/2
I'm happy to respond. (A) 1/4
(B) 1/3
(C) 2/5
(D) 5/4
(E) 3/2
As I discuss in this post,
https://magoosh.com/gmat/2012/gmat-work-rate-problems/
always add rates when machines work together.
basic system = A --- ventilates in 0.5 hr, so A's rate is (1 room)/(0.5 hour) = 2
more advanced system = B --- ventilates in 2 hr, so A's rate is (1 room)/(2 hour) = 0.5
Add rate --- combined rate = 2 + 0.5 = 2.5 rooms/hour = 5/2 rooms/hour
Now, how long would it take for a combo, ventilating at 5/2 rooms/hour, to ventilate a single room? We use the "ART" equation ----
A = RT --- that is, (amount) = (rate)*(time)
(1 room) = (5/2 rooms/hour)*T
1 = (5/2)*T
2/5 = T
So, the combo takes 2/5 of an hour to ventilate a room. Answer = (C)
Does this make sense?
Mike
11 Sep 2013, 00:13
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If you had to guess on this question, there are some ways to logically knock out a bunch of answers.
The two ventilation systems can clear the room in 1/2 hour and 2 hours, so combined they have to take less than 1/2 hour to do the job. Answers D and E are too big. Also, if both machines could do the job in 1/2 hour, then it would take 1/4 hour combined. Since the second machine takes 2 hours (and not 1/2 hour), then answer A is too small.
t1000
The two ventilation systems can clear the room in 1/2 hour and 2 hours, so combined they have to take less than 1/2 hour to do the job. Answers D and E are too big. Also, if both machines could do the job in 1/2 hour, then it would take 1/4 hour combined. Since the second machine takes 2 hours (and not 1/2 hour), then answer A is too small.
t1000
