Math question

[ponyfool]

If one machine can finish a job in 4 hours and another machine can finish the job in 2 hours, how long would it take for both machines to finish the job together?

This is a question that my wife's 3rd grade class is assigned, and I think the answer in their book is wrong. But, it's been years since I exercised this part of my brain, so maybe I'm wrong!

The first machine can do the 1/4 of the job per hour. The second machine can do 1/2 of the job per hour. Thus, adding them together, 1/4 + 1/2(2/4)= 3/4 of the job per hour, right?

Well, 3/4 of the job in one hour leaves 1/4 of the job. Since 1/4 is 1/3 of 3/4, that means it would take both machines 1/3 of an hour to do the remaining 1/4 of the job, right? Since 1/3 of an hour is 20 minutes, it would take both machines 1 hour 20 minutes, right?

The book says 1 hour 15 minutes and I think it's wrong. It should be 1 hour 20 minutes, right?

 

[exskibum]

You are correct, and the book is wrong.

 

[ponyfool]

I really hope that's the case cuz I am racking my brain trying to figure out how they got that answer. My only thought is, maybe they saw that it could do the job in 3/4 of an hour and figured that left 1/4 of an hour instead of 1/4 of the job.... pretty sloppy if you ask me for a text book.

Thankfully, my wife said that most of her students came up with 1 hour 20 min instead of the 1 hour 15 min. Pretty smart kids!

 

[madmike2]

Naw yuh doesn't wunna go a-messin' wiff dems tex-books. We pays em a lots uh munny tuh git the best peeple fer writin' en des-eye-nin' en edit-ee-fyin' dems books. En we pays'em lotsa munny to git thuh rite persons tuh due thuh seelectin' uh alla thems books soes alla ar yungin's el be abul tuh larn thems skilz tuh count en tuh wright guhd soe they'all kin goes tuh collage en bee smart en gets guhd jobs en all.

 

[painman]

They didn't say if the equipment were the same size......like my pappy said, I should a been a lawyer. PM. <><

 

[v65]

Well, 3/4 of the job in one hour leaves 1/4 of the job. Since 1/4 is 1/3 of 3/4, that means it would take both machines 1/3 of an hour to do the remaining 1/4 of the job, right? Since 1/3 of an hour is 20 minutes, it would take both machines 1 hour 20 minutes, right?

The percent of the job they can do in an hour times the total number of hours they work gives the percent of the job completed. You know the percent is 3/4, you want the time, x, so that the whole job is complete(100% or 1 as a decimal). So 3/4 x = 1, divide and x = 4/3. Thats the 7th grade solution

 

[Scab]

WTF? You bring us math!? Take a time-out and go sit in the corner.

 

[fjrchooser]

Actually the book is right. Competition - once they start working together gains them the 5 minutes, it's just human nature. Didn't they teach you guys anything in 3rd grade ? <_<

 

[odot]

Once I start drinking beer....it don't matter....because I won't be working it. Otherwise....if they don't figure it out soon....they smell like moist ass cheese.

 

[Groo]

Easy way to figure out the right answer.

1 of the machines does the job in 240 minutes. Therefore it does 1/240th of the total job every minute.

1 of the machines does the job in 120 minutes. Therefore it does 1/120th of the total job every minute.

Add that together and both machines are doing 1/80th of the job every minute (1/120th is equal to 2/240... so 2/240 + 1/240 = 3/240, which reduces to 1/80).

So then, if both machines working together do 1/80th of the job per minute.... it takes 80 minutes to finish... which is an hour and 20 minutes. QED.

 

[Bustanut joker]

Yeah Groo, but you forgot to add the time it takes to remove the part from one machine and put it in the other

:jester:

 

[OhioFJR1300]

and what about smoke breaks, restroom breaks and coffee breaks.

 

[MKO]

Easy way to figure out the right answer.
1 of the machines does the job in 240 minutes. Therefore it does 1/240th of the total job every minute.

1 of the machines does the job in 120 minutes. Therefore it does 1/120th of the total job every minute.

Add that together and both machines are doing 1/80th of the job every minute (1/120th is equal to 2/240... so 2/240 + 1/240 = 3/240, which reduces to 1/80).

So then, if both machines working together do 1/80th of the job per minute.... it takes 80 minutes to finish... which is an hour and 20 minutes. QED.

That was easy! Now can i take my 5 minute break before I start my next job?

 

[Rogue]

I explained it all earlier, here is the link again: Math

 

[FJRPierre]

I explained it all earlier, here is the link again: Math

LOL

 

[Longrifle]

I explained it all earlier, here is the link again: Math

Now I don't feel so stupid afterall....I thought my daughter's 3rd grade homework was pretty tough!

 

[user 2024]

Are these machines in a shop with union labor, in a US government shop, or south of the border in Mexico. Try that math!

 

[James Burleigh]

As a philosophy major I was naturally all over this. After an hour and a half and three sheets of paper, I got the wrong answer. So I asked my son lounging on the couch on break from his junior year as a physics major at Berkeley, if he wanted to try his hand at a really tough math problem. A few minutes later he said "An hour and 20 minutes." Okay, smarty pants, how'd you get that?

Turning the controls over to him (bear in mind I taught him everything he knows, about colors anyway):

Machine 1 does 1/4 a job per hour, Machine 2 does 1/2 a job per hour. X is the amount of time Machine 1 is allowed to work, Y is the time Machine 2 is allowed to work.
 
(1/4)/60min * X + (1/2)/60min * Y = 1
 
1/240min * X + 2/240min * Y = 1
 
1*X + 2*Y = 240min
 
The most efficient solution is when X = Y (both machines work for the full amount of time needed to complete the work)
 
X + 2X = 240min
 
3X = 240min
 
X = 80 minutes
 

 

[radman]

The funny part is the job consists of making parts for two trains.