Need some help with an Algebra question

[ptownTSI]

how long does it take two writers to do something?

George takes 8 hours to copy a 50 page manuscript while Sonya can copy the same manuscript in 6 hours. How many hours would it take them to copy a 100 page manuscript if they work together? Can you explain how to do this.

For some reason the correct answer as listed in my GMAT book is NOT 14 hours, because thats what I picked and got it wrong.

unless you can prove that it IS 14 hours, in which case the book is wrong.

[schmidty]

i think u might have misunderstood the question...they are workin on it together at the same time, not one after the other...

here's what I did

G =50pages / 8 hrs
S = 50 pages / 6 hrs

X = total hrs

(50pages/8hrs + 50pages/6hrs)*X hrs = 100pages
(300pages/48hrs + 400pages/48hrs)* X hrs = 100pages
(700pages/48hrs) * X hrs = 100pages
700pages * X = 4800pages
X hrs = 4800pages/700pages = 6.857 hrs

that right?

[LivingLegend06]

assuming that they are both working at the same time then they will both work the same ammount of hours until they are finished. this means that sonya will end up doing more than george.

50/8=6.25
50/6=8.333

6.25X=8.33
1.33=X <- this means sonya will do 1.33 times as many pages as george

1.33x + 1x = 100
(sonya pages) + (geroge pages) = total pages
x = 42.9 <- this means george will do 42.9 pages

42.9/6.25= 6.864 hrs

so yeah i got the same answer as schmidty.

[shiftbmw]

Simpler than that even. No need to go through the common denominator steps or anything.

Schmidty could have stopped at:

(50pages/8hrs + 50pages/6hrs)*X hrs = 100pages

[silversleeper]

i think algebra is fun, is that bad?

[schmidty]

i think algebra is fun, is that bad?

no...I secretly like it too :D

and shiftbmw...I was just goin step by step for ptowns benefit :D

[TwoJ's]

i think algebra is fun, is that bad?

I do as well. I actually enjoy most mathematics. Especially differential functions, and all calculus for that matter. This makes it easy for me to get a B.A. in Math at the same time as EE.

OP: What class is this for? And don't just say it's for math class.

[ptownTSI]

it was a GMAT review problem. no calculator, the correct answer is in fraction form 6 and 6/7 hours. kind of complicated, at least for me to do it like that.

[ptownTSI]

This is how I would have had to do it on the test. Let me know if you know of a short cut because you only have 75 minutes to do 37 problems, you really have to know what you are doing because many are like this is.

(50/8 + 50/6)x=100

get a common denominator of 48. multiply 50/8 by 6/6 and 50/6 by 8/8 and 100 by 48/48.

now we have

(300/48 ) + 400/48 )x= 4800/48

Therefore
( 700/48 )x= 4800/48

multiply both sides by 48/700 (dividing by a fraction)

so you get x= (4800/48 )*( 48/700)

the 48's cancel and you are left with 4800/700 which simplifies to 48/7

doing old school division 48 divided by 7; 7 goes into 48 6 times evenly. 6x7= 42. 48-42= 6

so you have a remainder of 6/7.

the total time is 6 and 6/7 hours.

I can do math!! its just been since oh geez about 8th grade since I did algebra problems like this. good brain refresher.

[equate975]

I always hated those questions, I knew they were super easy to do, but every time I learned the formula for it I instantly forgot it every time.

[TwoJ's]

This was more of a problem-solving problem. You have to look at it and create your own formula. These are the most fun/satisfactory.

And yeah, TSI that is the way to do it. It's almost identical to the way the others did it, just different styles. A lot of those steps can be combined. and yeah, if you are required to give an exact answer, then you probably want to get it in to fractions.

Or, if you can use a calculator and have a TI-89 or something similar then it will give you exact answers. TI-83's won't do that, and they are the most common calculators for lower level math classes.

Good luck!

[ptownTSI]

i have and can use a TI-89 well, much to the detriment of me actually learning calculus in fact. I wish I had never bought one of those in high school ap calculus because college calculus kicked MY ASS since i couldnt use a calculator anymore. This summer I'm going to try and retake pre-calc, so i can do calc 30 in the fall. (30 is standard engineering calculus at my university)

like i said this is for the GMAT and you cannot use a calculator with it.

its very easy to hit solve((50/8+ 50/6)x=100,x) on the ti-89. =48/7

makes for braindead answers though.

[e34john]

Heres how my old professor always taught those questions. Works for all kinds of those how much "work" problems.

George + Sonya = together
1 manuscript + 1 manuscript = 2(since its 100 pgs instead of 50)
------------ ------------- -----------------------------
8 hours + 6 hours = X

multiply each by the denominators 8,6,X to each numerator

so you will get 6X+8X=96
14X=96
--------
14

X=6.857 or 6 and 6/7 this way is easy because you can do it pretty fast without needing to do too much math or if you dont have a calculator.

The book is stupid it doesn't take into account that Sonya will pick up the slack after she does her 50 shes gonna have to keep going since they are working TOGETHER.

[325Projectz]

Best math problem ever.

[Jscotty]

Well lets look at it this way.. If they are using the same copier will they work together without getting in each other's way? Or perhaps George would slow Sonya down. Also if George is horny and Sonya is really hot, its anyone's guess as to how much time it will take if they work together.

And in all seriousness, having said all of that, some word problems are not always stuck directly to the exact caluclated answer. Many times the tests will ask you to find the "closest" answer or the "best" answer because an exact answer is not possible. Consider the following word problem:

Due to OSHA regulations, a laborer at a construction site is only permitted to lift a maximum of 100 lbs. How many men would it take to lift a piece of equipment that is 450 lbs?

If you did the exact calculations you would conclude that 4.5 men were needed to complete this task. But because there is no such thing as a half of a man, the answer would be 5.