Lesson: Work Questions

Comment on Work Questions

Hi Brent!

If 4 identical printing presses can complete a large printing job in 21 hours, how many presses would it take to do the job in 14 hours?

a numeric entry question.
greenlight-admin's picture

One approach is to assign a NICE VALUE to the job in question. We want a value that works well with 4 and 21 (numbers in the given information)

So, let's say that printing job consists printing a TOTAL of 84 pages (84 is divisible by 4 and 21)

If FOUR presses can print 84 pages in 21 hours, then ONE press can print 21 pages in 21 hours.

If ONE press can print 21 pages in 21 hours, then in ONE HOUR, a single press can print 1 page.

In other words, each press can print 1 page PER HOUR

"How many presses would it take to do the job in 14 hours?"

At a rate of 1 page per hour, ONE press can print 14 pages in 14 hours.

So, TWO presses can print 28 pages in 14 hours.

So, THREE presses can print 42 pages in 14 hours.


Since 84/14 = 6, we can conclude that SIX presses can print 84 pages in 14 hours.

Answer: 6 presses

I did it in this method but i am not certain whether the applied method is correct or not. please correct me if i am wrong.

if 4 printing presses can complete a job in 21 hours, then combined rate would be 4/x = 1/21 ( am assuming x hours that individual presses will work),
question is asking how many number of printing presses is required to complete same job in 14 hours, so
n/x = 1/14 from above x = 21*4, therefore n = (21 * 4)/14 = 6.

6 number of printing presses are required.
greenlight-admin's picture


Brent, I did basically the same thing, I assume, as yogasuhas (I might just be stating it differently). Except at the 4/x = 1/21 step I solved for x, and concluded that since x = 84, then each machine works at a rate of 1/84th per hour, or 1 machine will take 84 hours to do the job. Then I said, well, if each machine produces 1/84th per hour, how many machines will we need for a rate of 1/14th per hour (since you flip the rate to get the time required)? If I let the number of machines equal y, then we have, y(1/84) = 1/14. I solve for y, and get 6 machines. PS The picking a nice number method makes sense, I just have to get used to it.
greenlight-admin's picture

Nice work, Kevin. That solution is perfect!

this kind of questions are always tricky and I have had difficulties, while investing a lot of time during the test.

Practice questions with your solutions helps a lot!
THANK you!
greenlight-admin's picture

Good to hear!


Can you do a breakdown on how to solve this question? Thanks.
greenlight-admin's picture

This video was really helpful to understand these types of problems, thank you!

You showed a way to solve the first problem in the video using the O=RT formula and proportions. I know that the desert outpost problem is an inverse proportion - is there a way to also solve this problem with O=RT. I tried (below) but it was wrong, is this because O=RT does not work for inverse proportions?

O = RT
15 people = R(21 days)
R = 15/21

Since you use the same rate for the 9 people
O = RT
9 people = (15/21 rate) T
T = 12.6 days (WRONG)
greenlight-admin's picture

The easiest way to see the issue with your solution is to ask "What does a rate of 15/21 mean"
If we consider the terms, it means 15/21 people per day, which doesn't make any sense.

Having said that, we can still use the OUTPUT = (RATE)(TIME) formula to solve this question.

Let's let R = the rate at which ONE person drinks water (measured in cups per day).
So, if there are 15 people, the combined rate for all of them = 15R (in cups per day)
So, in 21 days, we can calculate the "OUTPUT" as follows:
OUTPUT = (15R)(21) = 315R

Key concept #1: The the combined rate for 9 people = 9R (in cups per day)
So, in X days, the "OUTPUT" for the 9 people is calculated as follows:
OUTPUT = (9R)(X) = 9RX

Key concept #2: The output (volume of water consumed) for the 15 people over 21 days will be equal to the output for 9 people over X days.
So, we can write: 315R = 9RX
Solve to get: x = 35

I'm having trouble with this question.. I can't seem to understand the relationship of how it takes 8 days to build 4 houses https://greprepclub.com/forum/qotd-4-if-it-takes-three-days-for-10-workers-to-finish-bu-2327.html I used the t=0/r formula.
greenlight-admin's picture

Question link: https://greprepclub.com/forum/qotd-4-if-it-takes-three-days-for-10-worke...

We can use time = output/rate
We just need to determine the rate of ONE worker.
Let's do that first...

Given: It takes 3 days for 10 workers to finish building 1 house
So, in 1 day, 10 workers can finish building 1/3 of a house
So, in 1 day, 1 worker can finish building 1/30 of a house

So, rate of ONE worker = 1/30 of a house per day
So, rate of 15 workers = 15/30 of a house per day
In other words, the RATE of 15 workers = 1/2 of a house per day

How many days will it take 15 workers to finish four houses?
We want an OUTPUT of 4 house

Time = output/rate
So, time = 4/(1/2) = 8 days

Does that help?



I used the ratio method suggested by you in the video.

4/120 = 5/x

to give x = 150

why am I not getting the correct answer?
greenlight-admin's picture

Question link: https://greprepclub.com/forum/if-four-boys-can-shovel-a-driveway-in-two-...

This isn't an equivalent ratios question.
Notice that 4 boys can can shovel a driveway in 120 minutes.
If we have 5 boys, we should be able to boys the driveway in LESS THAN two hours (since we have more workers).

Let's explore why using equivalent ratios won't work here.

IF we try to use equivalent ratios then:
8 boys can can shovel a driveway in 240 minutes
12 boys can can shovel a driveway in 360 minutes
400 boys can can shovel a driveway in 12000 minutes (over 8 days!)

This, as you can imagine, doesn't make sense. If we have 400 boys shoveling, the driveway would be cleared in a manner of seconds.

Does that help?


Hello Brent,
Please can you help me to understand better when we find the rate:
In the following question
Operating at the same constant rate, 4 identical machines can produce a total of 220 candles per minute. At this rate, how many candles could 10 such machines produce in 5 minutes?

I understand the approach
but when I tried to apply the formula

Rate=( output/time )
The rate will be 220 because the output per minute is 220 if I divide both I have 220. So when I replace this value here
I will have 11000=10*5*220

Using the value of that rate the result will be totally diferente I don’t know what I am missing while I am solving the problem with this method.

Thank you
greenlight-admin's picture

Question link: https://greprepclub.com/forum/operating-at-the-same-constant-rate-4-iden...

The rate of 220 candles per minute is the COMBINED rate for all 4 machines.
If you want to find the rate for ONE machine, you must divide 220 by 4 to get 55 candles per minute

This value of 55 candles per minute will yield the correct answer.

Cheers, Brent


Hi Brent,

I approached the above mentioned question a bit differently than you did on on greprepclub.
I would just like to check whether my way of thinking is ok.
So in the beginning of the exercise I assume that the job is 12.
After that I calculate the rate for Audrey 12/4=3 and the rate for Ferris 12/3=4.
Then to get the rate at which they would finish the job, had there not been any breaks, 12/7=1,714.
Then I just subtract that from the real time that they needed for the job with the breaks and I get 2-1,714=0,286. I divide the mentioned remainder with 3 and get roughly 0,1.
Would that be ok, or did I just get lucky.
Thank you!
greenlight-admin's picture

Question link: https://greprepclub.com/forum/rates-and-work-question-14025.html

Your answer of 0.1 represents 0.1 HOURS, which is equal to 6 minutes, which is incorrect.
Your calculation would be correct if BOTH people stopped working during the breaks. However, Ferris is the only person who stopped working.

Let's do as you say and let the entire job = making 12 widgets

Notice that, if BOTH people stopped working for 0.286 hours, then the LOSS of production = (0.286)(7) = 2 widgets

Aside: lost time = 0.286 and their COMBINED rate = 7 widgets per hour.

Since ONLY FERRIS stopped working during this time, we need to determine the time it would have taken Ferris to make 2 widgets.
FERRIS' rate = 4 widgets per hour
So, the time for Ferris to make 2 widgets = 2/4 = 0.5 hours.
So, Ferris' 3 breaks must add to 0.5 hours (30 minutes)

So, each break must have been 10 minutes.

That's that help?

Oh I see where I erred.
Thank you for pointing it out.
It is funny how I make mistakes like this sometimes, yet, luckily, I end up with the correct answer haha.
greenlight-admin's picture

Yes, that happens once in a while :-)
It's like slicing a golf ball into the forest only to have it bounce off a tree and land on the green!

I just cannot for the ***king life of me understand this question:

I can totally understand how to do work questions that involve 2 people, like if Sam can do 1 job in 3 hours at his rate and Sue can do 1 job in 5 hours at her rate, how long will it take to do them together..That's my kind of work question? The one in the link is filthy and disgusting. I really hope I don't encounter that on my take-home GRE because I'll curse out loud and give the proctors the middle finger. The logic is totally nuts and I cannot grasp it, so I will have to just guess and move on. Pray that I don't encounter this kind of work question on the test or I will go psychotic! (This standardized test already makes me very mentally unstable, and if I get a low score, I'm writing about this in my law school addenda. These tests MUST be done away with)
greenlight-admin's picture

Question link: https://greprepclub.com/forum/qotd-13-three-pumps-p-r-and-t-working-simu...

Everybody has topics they find easy and topics that confound them. A common response is to avoid the difficult questions (and even suggest that they're too difficult to be actual GRE questions), when a more productive response would be to learn the required concepts and strategies and answer practice questions until you've mastered them.


I am solving this rates problem: https://greprepclub.com/forum/working-together-at-their-respective-constant-rates-robot-a-9896.html.

I attempted to solve it by the following:
(1/A) + (1/B) = 88 / 6
(1/(0.6*B)) + (1/B) = 88 / 6
(5/3B) + (3/3B) = 88 /6
(8 / 3B) = 88 /6
B = (88 / 6) * (3 / 8) = 11/2
A = (3 / 5) * 11 / 2 = 33 / 10
165 * (10 / 33) = 50

Can you please explain where I went wrong? Thanks so much!
greenlight-admin's picture

Question link: https://greprepclub.com/forum/working-together-at-their-respective-const...
I'll answer your question with two questions:
1) What do A and B represent?
2) What do 1/A and 1/B represent?
I'll believe your see the issue when you answer those questions.

In the meantime, I suggest that you let A = robot A's RATE (in gemstones per minute) and let B = robot B's RATE (in gemstones per minute) and go from there.
If you need any additional help, my full solution is here: https://greprepclub.com/forum/working-together-at-their-respective-const...


I solved this problem an algebraic way and got it right, I wanted to know if there is a way to choose numbers for the distance perhaps and being able to solve it. My first instinct was to try numbers but it didnt work out, so I resorted to algebra. Thanks!
greenlight-admin's picture

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