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Two machines are sawing wood but due to space limitations [#permalink]

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14 Nov 2008, 14:26

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Two machines are sawing wood but due to space limitations only one at a time can operate. Machine A is used for the first shift and the other machine for the second shift, while both work half of the third shift. Machine A can do the job in 12 days if it worked two shifts and Machine B can do the job in 15 days if it worked two shifts. How many days will it take to do the job with current work schedule?

A = 1/12 of the work in 1 day working 2 shifts B = 1/15 of the work in 1 day working 2 shifts

If you cut the # of shifts to 1 each, that's cutting the rate in half, so you'd only get 1/2 the work done in 1 day for 1 shift

A = 1/24 of the work in 1 day on 1 shift B = 1/30 of the work in 1 day on 1 shift.

Together, they get \(\frac{1}{24} + \frac{1}{30}\) of the work done in 2 shifts.

1/24 + 1/30...find a common factor...120. So 1/24 = ?/120 = 5/120 and 1/30 = ?/120 = 4/120 so 9/120 in 2 shifts...but they each get another 1/2 shift. so half of 9/120 is 4.5/120 (yes, I know it's not good to use decimals, but it will make sense the ease of use in a second). so 13.5/120 is the same as 17/240. This should be the amount of work the machines can do together in 1.5 shifts each per day.

now 240/17 gives us just over 14, meaning it won't quite finish all of the work in 14 days, but that's the closest we have for an answer.

I answer A, but am not 100% sure about it.

bigfernhead wrote:

Two machines are sawing wood but due to space limitations only one at a time can operate. Machine A is used for the first shift and the other machine for the second shift, while both work half of the third shift. Machine A can do the job in 12 days if it worked two shifts and Machine B can do the job in 15 days if it worked two shifts. How many days will it take to do the job with current work schedule?

14 13 11 9 7

_________________

------------------------------------ J Allen Morris **I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$.

Wow. I'm having that kind of day today. 13.5/120 = 17/240???? Somedays are great...others you should break the alarm clock and sleep for another 24 hours.

rjacobs wrote:

jallenmorris wrote:

so 13.5/120 is the same as 17/240. This should be the amount of work the machines can do together in 1.5 shifts each per day.

now 240/17 gives us just over 14, meaning it won't quite finish all of the work in 14 days, but that's the closest we have for an answer.

I answer A, but am not 100% sure about it.

Hey jallen, it's me again, the a**hole that keeps correcting your math! 13.5/120 = 27/240 (not 17/240). 240/27 ≈ 8.8, so 9 is my answer.

That having been said, I don't think this would show up on the GMAT...the numbers are too confusing, as are the directions.

_________________

------------------------------------ J Allen Morris **I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$.

Each machine works an equal 1.5 shifts per day, so just average their productivities: 13.5 days working two shifts. However, they work 3 shifts, so 13.5 * 2/3 = 9.

Your method works for very simple problems, but the method of using 1/24 and 1/30 is a better approach to handle more complex problems that might be seen on the actual GMAT. My explanation is that detailed to allow the most people to understand it and get value from it. Not everyone that browses these questions and answers wants or needs a 700+ for their business school of choice.

phdizzle wrote:

Whoaaa dudes too much math!

Each machine works an equal 1.5 shifts per day, so just average their productivities: 13.5 days working two shifts. However, they work 3 shifts, so 13.5 * 2/3 = 9.

_________________

------------------------------------ J Allen Morris **I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$.

hey jallen--All I was trying to do is show a way that you could save time on the test. Wasn't trying to make any assumptions about who was reading. In any case, the only thing you have to do to generalize what I did is calculate a weighted average if the two machines don't work equal shifts. In that case, it's (weighted average)*2/3. Say, for example, A works half a shift and B works the other 2.5 shifts:

(0.5)/3 * 12 + 2.5/3 * 15 would be the new rate, or 14.5 days. Then you'd multiply that by 2/3 to get a nasty decimal that would be the final answer.

Wow. I'm having that kind of day today. 13.5/120 = 17/240???? Somedays are great...others you should break the alarm clock and sleep for another 24 hours.

rjacobs wrote:

jallenmorris wrote:

so 13.5/120 is the same as 17/240. This should be the amount of work the machines can do together in 1.5 shifts each per day.

now 240/17 gives us just over 14, meaning it won't quite finish all of the work in 14 days, but that's the closest we have for an answer.

I answer A, but am not 100% sure about it.

Hey jallen, it's me again, the a**hole that keeps correcting your math! 13.5/120 = 27/240 (not 17/240). 240/27 ≈ 8.8, so 9 is my answer.

That having been said, I don't think this would show up on the GMAT...the numbers are too confusing, as are the directions.