Machine M,N,O working simultaneously

[lizishao]

To Selyth,

What's wrong with my explanation? Please see it clearly before comments.

Total Unit produced = 4/3X + X +2/3X = 3X

What is the meaning by
IMO correct answer, but wrong notation:
4x/3+3x/3+2x/3=3x
9x/3=3x
3=3

[selytch]

Originally Posted by lizishao

To Selyth,

What's wrong with my explanation? Please see it clearly before comments.

Total Unit produced = 4/3X + X +2/3X = 3X

What is the meaning by
IMO correct answer, but wrong notation:
4x/3+3x/3+2x/3=3x
9x/3=3x
3=3

No offense
I was trying to solve your equation
4/3X + X +2/3X = 3X
which is 3x=3x
but then realized it was not an equation but
3X=total units produced.
You went with fixed time, I used fixed amount.
Both ways are valid.

[lizishao]

Originally Posted by selytch

No offense
I was trying to solve your equation
4/3X + X +2/3X = 3X
which is 3x=3x
but then realized it was not an equation but
3X=total units produced.
You went with fixed time, I used fixed amount.
Both ways are valid.

Actually, I feel a little offense. Because I am quite confident in my math, just as you do.

[selytch]

Originally Posted by lizishao

Actually, I feel a little offense. Because I am quite confident in my math, just as you do.

I'd say you are better

[lizishao]

"Flatter Me, and I May Not Believe You. Criticize Me, and I May Not like You. .... Encourage Me, and I Will Not Forget You."

[wawan_andrean]

OA is B

[clock60]

agree with B as we need ratio we can deal with actual numbers
let be x=24. and time for O to complete order 12
rate of O=24/12=2
for N, 12*2/3=8-time for N to complete and rate will be 24/8=3
for M 8*3/4=6-time for M to complete and rate will be 24/6=4
in 1 hour together they will make
2+3+4=9-total
N-wil make 3
3/9=1/3-so B

[arindambanerji]

B for me as well 1/3

[Zealot]

Originally Posted by wawan_andrean

Machine M can produce x units in 3/4 of the time it takes machine N to produce the same amount of units. Machine N can produce x units in 2/3 the time it takes machine O to produce that amount of units. If all three machines are working simultaneously, what fraction of the total output is produced by machine N?

A. 1/2
B. 1/3
C. 4/13
D. 8/29
E. 6/33

My solution

Let
O=1
N=2/3
M=3/4(2/3)=1/2

When working together the rate is 1+3/2+2=9/2
Proportion of N=3/2 of 9/2 = 1/3

[stantheman]

Remember that W = R * T

Set W = 12

Machine O: Set T(O) = 6, thus R(O) = 12/6 = 2
Machine N: Set T(N) = 6*(2/3) = 4, thus R(N) = 12/4 = 3
Machine M: Set T(M) = 4*(3/4) = 3, thus R(M) = 12/3 = 4

R(M+N+O) = 2 + 3 + 4 = 13

W = 12 = 13 * T, thus T(M+N+O)= 12/13

How much work does Machine N do in T = 12/13?
W = 3*12/13 = 36/13

Fraction of Total Work?

(36/13)/12 = 36/13*1/12 = 4/13

Note: someone made a mistake in their additions of fractions:
2/1 + 2/2 + 3/2 = 7/2 not 9/2. When you guys switch, you get the wrong answer.