Machines X and Y run at different constant rates, and machine X can co

Another way to solve this question is to assign a nice value to the job.
So, we want to use a value that works well with the given numbers in the question (9, 3 and 4 hours).
Since 36 is the least common multiple of 9, 3 and 4, let's say the entire job consists of making 36 widgets

Machine X can complete a certain job in 9 hours
So, Machine X's RATE = 36/9 = 4 widgets per hour

Machine X worked on the job alone for the first 3 hours and the two machines, working together, then completed the job in 4 more hours.
At its rate of 4 widgets per hour, Machine X would have produced 12 widgets in 3 hours
36 - 12 = 24
So, after the first 3 hours, the two machines would need to produce the 24 remaining widgets in the job

Since the two machines COMBINED produced the remaining 24 in 4 hours, their COMBINED RATE = 24/4 = 6 widgets per hour

We can write: (Machine X's rate) + (Machine Y's rate) = 6 widgets per hour
Substitute to get: 4 + (Machine Y's rate) = 6 widgets per hour
From this, we can see that Machine Y's rate = 2 widgets per hour

How many hours would it have taken machine Y, working alone, to complete the entire job?
time = output/rate
So, time = 36/2 = 18

Answer: A

Cheers,
Brent

Machine Y does (1-7/9) = 2/9 of the job in 4 hours.
Therefore machine Y will do total job in 9/2 ×4 = 18 hours

Option A is the answer.

Posted from my mobile device

Hi, i did as follows:

3/9+4(1/9+1/y)=1
3 hours A alone and then 4 hours both together equals 1

im not getting an answer with this though. could some help point the error?

A 20 second approach:

Formula for this case, y = xt/(x-p-t), where, y = time needed by y alone, x=time needed by x alone, p= time needed for partial work done by x and t= time needed together after x.

So, y = 9*4/(9-3-4) = 18 hours. [A]

Machine X rate = 1/9

1/9 * 3 = Machine X completed 1/3 of the job

Machine X and Y then worked together for 4 more hours. In those 4 hours, Machine X will complete 4/9 of the job

3/9 + 4/9 = Machine X competed 7/9 of the job

In 4 hours, Machine Y completed 2/9 of the job

2/9 = 4/18

Machine Y's rate is 1/18 (18 hours to complete the job). Answer is C.

3/9+4(1/9+1/y)=1
Should be
4(1/9+1/y)=1-3/9
Because 3/9 is the work that has already been done

let machine Y took y hrs. alone to complete the whole job

Give, for X is 9 hrs. ( individual time taken)
Let, total unit of job = LCM of 9 & y = 9y

X # machine ---> 9 hrs( individual) --> rate = y unit /hr
Y # machine ---> y hrs( individual) --> rate = 9 unit /hr

So, per hr X machine will do --> y unit job
Y machine will do --> 9 unit of job
So, according to question:
3y+4y+36 = 9y
y = 18
Ans. A

Make Rate questions easier by plugging in a value for Work.
Let work be 36 (LCM of 9, 3, and 4)

Use the formula: W = R x T

Machine X: 36 = R X 9 => R = 4

Work done by Machine X in 3 hours = 4 x 3 = 12

Amount of Work left = 36 - 12 = 24

Now, work done by both the machines in 4 hours to complete the work = (4 + a) x 4 ;where 'a' is the rate of Machine Y

Therefore, 24 = 4 (4 + a)
a = 2

Hence, time taken by Machine Y to complete the work = Work/Rate = 36/2 = 18

Answer - A

The ratio of Time for work (X:Y: X+Y) = 9:? : 6
How did we get 6 hours?
X can complete the same job in 9 hours, so in 3 hours it can complete 1/3 of the job,
Now X and Y together do 2/3 of the job in 4 hours. What it means is that they can complete the job from start in 6 hours. That's how we got 6 hours
So the ratio of time for
X:X+Y = 9:6 = 3:2
The ratio of rate for X: X+Y will be 2:3
Since rates are additive, Ratio of rates for X:Y:X+Y = 2:1:3
So, Ratio of time for X:Y = 1:2
That is Y takes twice time as many as X takes time to complete the job
Since X takes 9 hours, Y will take 18 hours to do the job alone.

I never know when I should just type in the values and when it's better to solve algebraically. Any suggestions?

Machine X did 1/3 of the Job at the rate of 1/9hrs

Rate = Work / Time

Work Remaining: 2/3 | Time: 4 hours

Combined Rate: 2/3 / 4 = 1/6hours
Subtract Combined Rate with Rate of X to get Rate of Y

1/6 - 1/9 = 1/18 hours