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# Working alone at it's own constant rate, a machine seals K

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Manager
Joined: 13 Dec 2005
Posts: 64
Followers: 1

Kudos [?]: 3 [0], given: 0

Working alone at it's own constant rate, a machine seals K [#permalink]  03 Jan 2006, 17:45
Working alone at it's own constant rate, a machine seals K cartons in 8 hours, and working alone at it's own constant rate, another machine seals K cartons in 4 hours. If the two machines, each working alone at it's own constant rate and for the same period of time, together sealed a certain number of cartons, what percent of the cartons were sealed by the machine working at the faster rate?

A) 25%
B) 33 and 1/3%
C) 50%
D) 66 and 2/3%
E) 75%
SVP
Joined: 05 Apr 2005
Posts: 1733
Followers: 5

Kudos [?]: 37 [0], given: 0

Re: Work Question [#permalink]  03 Jan 2006, 18:42
ellisje22 wrote:
Working alone at it's own constant rate, a machine seals K cartons in 8 hours, and working alone at it's own constant rate, another machine seals K cartons in 4 hours. If the two machines, each working alone at it's own constant rate and for the same period of time, together sealed a certain number of cartons, what percent of the cartons were sealed by the machine working at the faster rate?

D) 66 and 2/3%

D. faster machine can do k in 4 hours
faster machine can do 2k in 8 hours
slower machine can do k in 8 hours
(faster + slower) machine can do (2k+k) in 8 hours

% of cartoons faster machine does = 2k/3k=2/3 of total or 67%
Director
Joined: 04 Oct 2005
Posts: 587
Location: Chicago
Followers: 1

Kudos [?]: 5 [0], given: 0

In 1 hr Machine A does k/8 cartons
In 1 hr Machine B does k/4 cartons (B is faster)

Lets dsay both worked for time t
means kt/8(A) +kt/4(B)=3kt/8 (total cartons)

Carton done by B/Total cartons =(kt/4)/(3kt/8)*100= 200/3=66 and 1/3%
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