GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Machine X if operating alone takes 10 hours to complete a job. Machine
[#permalink]
03 May 2022, 01:00
03 May 2022, 01:00
1
Expert Reply
2
Bookmarks
00:00
Question Stats:
56% (02:21) correct
43% (02:55) wrong based on 32 sessions
Hide Show timer Statistics
Machine X if operating alone takes 10 hours to complete a job. Machine Y starts the job one hour after Machine X started the job and X and Y together complete the job in 7 hours. How long does it take for Machine Y to complete the job if it had operated alone?
A. 20 hours
B. 25 hours
C. 31.5 hours
D. 32 hours
E. 35 hours
A. 20 hours
B. 25 hours
C. 31.5 hours
D. 32 hours
E. 35 hours
Part of the project: GRE Quantitative Comparison & Problem Solving Challenge
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
GRE Math Essentials for a TOP Quant Score - Q170!!! (2021)
GRE Geometry Formulas for a Q170
GRE - Math Book
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
GRE Math Essentials for a TOP Quant Score - Q170!!! (2021)
GRE Geometry Formulas for a Q170
GRE - Math Book
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: Machine X if operating alone takes 10 hours to complete a job. Machine
[#permalink]
03 May 2022, 05:33
03 May 2022, 05:33
3
Carcass wrote:
Machine X if operating alone takes 10 hours to complete a job. Machine Y starts the job one hour after Machine X started the job and X and Y together complete the job in 7 hours. How long does it take for Machine Y to complete the job if it had operated alone?
A. 20 hours
B. 25 hours
C. 31.5 hours
D. 32 hours
E. 35 hours
A. 20 hours
B. 25 hours
C. 31.5 hours
D. 32 hours
E. 35 hours
For work questions when the "job" is not defined, I find it easiest to assign a nice value to the job.
In this case, I want to find a nice value that works well with the given information (10 hours and 7 hours)
So, let's say the job consists of making a total of 70 widgets (notice that 70 is the least common multiple of 10 and 7)
Given: Machine X if operating alone takes 10 hours to complete a job.
In other words, working alone, Machine X can make 70 widgets in 10 hours.
Rate = output/time
So, Machine X's rate = 70/10 = 7 widgets per hour
Given: Machine Y starts the job one hour after Machine X started the job and X and Y together complete the job in 7 hours.
In the first hour (while working alone), machine X produces 7 widgets.
70 - 7 = 63
So, when Machine Y starts helping, the two machines must make 63 widgets in order to complete the job.
We're told the two machines (working together) complete the job in 7 hours.
Rate = output/time
So the COMBINED rate of the two machines = 63/7 = 9 widgets per hour.
Machine X's rate = 7 widgets per hour
So, we can conclude that Machine Y's rate = 2 widgets per hour
Question: How long does it take for Machine Y to complete the job if it had operated alone?
Time = output/rate
So, the time = 70/2 = 35 hours
Answer: E
Machine X if operating alone takes 10 hours to complete a job. Machine
[#permalink]
26 Sep 2023, 14:50
26 Sep 2023, 14:50
Shouldn't the answer be A?
From the question, I understand that X worked for 1 hour, and then both X and Y finished the work together.
And the total time it took them is 7 hours (this is the confusing part for me in this question).
I used a formula approach.
X rate - 1/10
Y rate - r
(1/10)*1 + (1/10 + r)*6 = 1
7/10 + 6r = 1
7 + 60r = 10
60r = 3
r=3/60=1/20
time = 20/1 = 20 hours.
From the question, I understand that X worked for 1 hour, and then both X and Y finished the work together.
And the total time it took them is 7 hours (this is the confusing part for me in this question).
I used a formula approach.
X rate - 1/10
Y rate - r
(1/10)*1 + (1/10 + r)*6 = 1
7/10 + 6r = 1
7 + 60r = 10
60r = 3
r=3/60=1/20
time = 20/1 = 20 hours.
