Work Rate Problem

[oxvt]

Working at its own constant rate, a machine seals k cartons in 8 hours, and working alone at its own constant rate, a second machine seals k cartons in 4 hours. If the two machines, each working at its 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 1/3%
C) 50%
D) 66 2/3%
E) 75%

[bluementor]

Machine A seals k cartons in 8 hours
Machine B seals k cartons in 4 hours
Clearly, Machine B is the faster machine here.

For a certain period of time, say 8 hours:

Machine A would have sealed k cartons
Machine B would have sealed 2k kartons

%cartons sealed by B = 2k/(2k+k) = (2/3)*100% = 66 2/3% Choose D.

You will see that this fraction stays the same regardless of time-period you pick.

-BM-

[marcusking]

Working at its own constant rate, a machine seals k cartons in 8 hours, and working alone at its own constant rate, a second machine seals k cartons in 4 hours. If the two machines, each working at its 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 1/3%
C) 50%
D) 66 2/3%
E) 75%

Machine A: 1/8
Machine B: 1/4
Total produced: 1/8 + 1/4 => 3/8

Machine B is responsible for 1/4 of the total work completed which we just calculated as 3/8.

(1/4)/(3/8) => (1/4)*(8/3) => 8/12 => 2/3 or 66 2/3%
D.

[krisraam]

Same amount of work is done by A in 8hrs
Same amount of work is done by B in 4hrs

Clearly B is faster than A by 100%

If both A and B work for same time. B will end up doing double the work of A.

ie 2/3 of the work = 662/3%

Thanks
raama

[bhumika.k.shah]

thanks for the different approaches guys
it really helps coz u may never know which one strikes to u during D day

[missrochelle]

Quick question here.... sometimes when we are calulating a % of something we multiply them.

16% OF 100 ====> .16 * 100

But here, we divided. 1/4 OF 3/8 ..... instead of multiplying.

Can someone explain why? I got that far, but then multiplied (1/4 times 3/8) so am a bit confused why we are to divide.

[silvi]

@ missrochelle

the question stated that what percent of the cartons were sealed by the machine working at the faster rate?
it means

cartoons sealed by Machine B / (cartoons sealed by both {Machine A + Machine B}) * 100

so, it's {1/4} / {3/8} * 100 = > 2/3* 100 => 662/3%

Thanks
Silvi