Achiever 2 QR #23

[tawaqul]

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It says: Thom can finish painting in 4hrs while Joe has to take 3 times as long for the same job. What is Bill's speed of work compared to Thom if it only takes 1.2 hours for all to jointly finish?

Answer: 2 times as fast.

Now, normally when I do these types of problems, I use the work formula AB/A+B, but here it doesn't work for some reason, maybe ABC/A+B+C messes it up, not sure. Anyways, can someone explain why this formula doesn't work and explain the problem to me? I can't figure out how to work it out simply--if that's possible!

Thanks!🙂

 

[Andre3k]

It says: Thom can finish painting in 4hrs while Joe has to take 3 times as long for the same job. What is Bill's speed of work compared to Thom if it only takes 1.2 hours for all to jointly finish?

Answer: 2 times as fast.

Now, normally when I do these types of problems, I use the work formula AB/A+B, but here it doesn't work for some reason, maybe ABC/A+B+C messes it up, not sure. Anyways, can someone explain why this formula doesn't work and explain the problem to me? I can't figure out how to work it out simply--if that's possible!

Thanks!🙂

Tom- 1/4

Joe- 1/12

Bill- 1/x

Total- 1/1.2

1/4 + 1/12 + 1/x = 1/1.2
3/12 + 1/12 + 1/x = 10/12
1/x = 1/2
x=2 So Bill does it in 2 hours twice as fast as Tom

 

[tawaqul]

where did that formula come from though? the 1/T 1/ B etc...how would I know to do that?

The way you did it looks simple enough, I just don't exactly "get" it. If you could explain a little more, I would appreciate it...I've never been good at math! 🙄

 

[211183]

where did that formula come from though? the 1/T 1/ B etc...how would I know to do that?

The way you did it looks simple enough, I just don't exactly "get" it. If you could explain a little more, I would appreciate it...I've never been good at math! 🙄

I believe he is saying that the 1/4 means....

That guy (forget his name)... can do the job in 4 hours... so in 1 hour, he can do 1/4 of the job.

THe other guy... can do the job in 12 horus... so in 1 hor... he can do 1/12 of the job....

does that clear it up at all? 😳

 

[tawaqul]

yeah, that makes sense. But does anyone know why my original equation DOES NOT work? I learned it in Kaplan the AB/A+B thing...

 

[211183]

you have to know that

ab/a+b doesn't work if you just add another thing to it..

you can't make it

abc/a+b+c

you have to do

ab/a+b... then find the answer... then do that times the new one.




someone confirm?

 

[211183]

yea i just did the math and it works my way....
i use the same formula as you..
but don't make the mistake of thinking you can just add terms... work formula only works with two things...

you get

4*12 / 4 + 12 = 3


then you do

3x / 3+x = 1.2

that works out to 2 i believe

 

[tawaqul]

great thanks!

 

[Andre3k]

where did that formula come from though? the 1/T 1/ B etc...how would I know to do that?

The way you did it looks simple enough, I just don't exactly "get" it. If you could explain a little more, I would appreciate it...I've never been good at math! 🙄

1/4 comes from saying he can do 1 job in 4 hours or 1job/4hours (1/4) and the other dude can do 1job in 12 hours or 1job/12hours (1/12).
Bill is 1/x and the total is 1/1.2

1/4 + 1/12 + 1/X= 1/1.2 👍

Most of these problems work like this,

 

[klutzy1987]

1/4 comes from saying he can do 1 job in 4 hours or 1job/4hours (1/4) and the other dude can do 1job in 12 hours or 1job/12hours (1/12).
Bill is 1/x and the total is 1/1.2

1/4 + 1/12 + 1/X= 1/1.2 👍

Most of these problems work like this,

The stndard equation is 1/x + 1/y + 1/z + 1/(etc..) = 1/T
x,y,z and (etc..) are all variables representing individual times.

T is the total time that it would take if they all work together.

This works because in reality you are caculating the amount of work they can do in one hour and calculating the total work done by all of the people in one hour. Then you are just calculating how many hours it would take to do all of the work or T.