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

Question

Machines X and Y run at different constant rates, and machine X can complete a certain job in 9 hours. 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. How many hours would it have taken machine Y, working alone, to complete the entire job?

(A) 18
(B) 13 1/2
(C) 7 1/5
(D) 4 1/2
(E) 3 2/3

PS56502.01

(A) 18 
(B) 13 1/2 
(C) 7 1/5 
(D) 4 1/2 
(E) 3 2/3

PS56502.01

Archit3110 · Accepted Answer

rate of X = 1/9
completed work 1/9 * 3 ; 1/3 job 
left with 2/3 work which is completed in 4 hrs more working together X&Y ;
2/3 = (1/9+1/y)*4
solve y=18 
IMO A

CareerGeek · Answer

Let Y alone takes 'a' hours to complete

Fraction of Work done by X in 3 hours = 3/9 = 1/3
Remaining 4 hours, work by X & Y together = 4/9 + 4/a

--> 1/3 + 4/9 + 4/a = 1
--> 7/9 + 4/a = 1
--> 4/a = 2/9
--> a = 18

IMO Option A

Pls Hit kudos if you like the solution

BrentGMATPrepNow · Answer

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

gurmukh · Answer

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

Kritisood · Answer

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?

nazmul2016 · Answer

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.

Basshead · Answer

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.

plaverbach · Answer

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

bobnil · Answer

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

DeeptiManyaExpert · Answer

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

brains · Answer

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.

Schachfreizeit · Answer

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

muhammaddk92 · Answer

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

egmat · Answer

Here's how to think about this:

Step 1: Understand Machine X's rate

Machine X can complete the job in 9 hours. So think about it this way - if X finishes the entire job in 9 hours, then every hour X completes  \frac{1}{9}  of the job.

This is the foundation of work rate problems:  Rate =  \frac{1}{	ext{time to complete}}

Step 2: Calculate how much work X did alone

Machine X worked alone for the first 3 hours. Let's figure out how much of the total job got done:

Work done by X alone =  3 	imes \frac{1}{9} = \frac{3}{9} = \frac{1}{3}

So after X worked alone for 3 hours,  \frac{1}{3}  of the job is complete. This means  \frac{2}{3}  of the job still remains.

Step 3: Set up the equation for combined work

Here's the key insight: X and Y then work together for 4 hours to finish that remaining  \frac{2}{3}  of the job.

During these 4 hours:
 
 Machine X continues at its rate of  \frac{1}{9}  per hour, so X completes  4 	imes \frac{1}{9} = \frac{4}{9}  of the total job 
 Machine Y works at rate  \frac{1}{t}  per hour (where  t  is what we're looking for), so Y completes  4 	imes \frac{1}{t} = \frac{4}{t}  of the total job

Together, they must complete exactly  \frac{2}{3}  of the job:

\frac{4}{9} + \frac{4}{t} = \frac{2}{3}

Step 4: Solve for t

Let's isolate the term with t:

\frac{4}{t} = \frac{2}{3} - \frac{4}{9}

Converting to common denominator (9):

\frac{4}{t} = \frac{6}{9} - \frac{4}{9} = \frac{2}{9}

Now cross-multiply:

4 	imes 9 = 2 	imes t 
 36 = 2t 
 t = 18

Answer: (A) 18 hours

Notice the logic here: Y is slower than X (takes 18 hours vs. 9 hours), which makes sense because even with Y's help, it still took 4 hours to complete the remaining  \frac{2}{3}  of the job.

Want to master work rate problems systematically?

The approach I showed you works, but there are faster techniques and patterns that apply across all work rate problems. You can check out the  complete solution on Neuron by e-GMAT  to understand the systematic framework for all work rate variations, including the common traps you need to avoid and alternative approaches that can save you time. You can also explore detailed solutions for  other official GMAT questions on Neuron  with comprehensive practice and analytics on your specific weaknesses.

Hope this helps!

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards