GMAT Question Patterns: Work and Rate Problems

Question

We reviewed questions from the GMAT Prep Tests and Official Guide 2024–2025 to identify the most common patterns involving distance and speed.

This guide focuses on the types of Work and Rate problems you may encounter on test day.

The goal of this project is to uncover as many recurring question types as possible, for three key reasons:

Get a higher score – Master each pattern so you don’t miss out on easy points. 
 Save time – No need to do hundreds of questions; just a few from each pattern will do. 
 Peace of mind – Be confident that you've covered all known question types.

Work and Rate problems appear in both the Problem Solving and Data Sufficiency sections of the GMAT Focus Edition. In total, there are 23 Problem Solving and 9 Data Sufficiency questions involving these concepts, based on GMAT Prep Focus and OG 2024–2025. Worth noting that Work and Rate concepts can also appear in DI sections such as Graph Interpretation, Tables, Two-Part Analysis, or Multi-Source Reasoning.

Note: 
 
  The questions in this guide are drawn from the Official Guides and GMAT Prep (Focus).

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Pattern #1: Single Entity Working Alone   
 - A scenario where one worker (person, machine, or system) completes a task independently without any assistance.

Example 1.1 (Difficulty: 505 Level)

If Benny read for 3 hours and t minutes at an average rate of 36 pages per hour, which of the following represents the number of pages that he read?

(A)  36t 
(B)  36 + t 
(C)  36 + 5t 
(D)  108 + \frac{3t}{5} 
(E)  108 + \frac{t}{5}

Question Discussion .

Example 1.2 (Difficulty: 505 Level)

When water is flowing into a certain pool at the rate of r gallons per hour, it takes 9 hours to fill the pool. In terms of r, how many hours will it take to fill the pool if water is flowing into the pool at the rate of r + 5 gallons per hour?

A.  \frac{9(r + 5)}{r} 
B.  \frac{r + 5}{9r} 
C.  \frac{r}{r + 5} 
D.  \frac{9r}{r + 5} 
E.  \frac{r}{9(r + 5)}

Question Discussion .

Example 1.3 (Difficulty: Sub 505 Level)

If snow accumulation increased at a constant rate of 30 millimeters per hour during a certain snowstorm, how many seconds did it take for snow accumulation to increase by 1 millimeter?

A. 1/120
B. 1/60
C. 1/20
D. 20
E. 120

Question Discussion .

Example 1.4 (Difficulty: 605 Level)

Water flows into an empty swimming pool at a constant rate of 50 liters per minute. If the pool's total capacity is 120 cubic meters, approximately how many hours does it take until the pool is filled to 2/3 of its total capacity? (1 liter = 1,000 cubic centimeters)

A. 7
B. 13
C. 27
D. 40
E. 53

Question Discussion .

Example 1.5 (Difficulty: 705 Level)

On June 8, 2008, a computer set a speed record by completing arithmetic operations at a rate of approximately 1.026 x 10^15 operations per second. At this rate, which of the following is closest to the fraction of an hour it would take this computer to complete 1 million mega-operations, if 1 mega-operation is defined to be 1 million arithmetic operations?

A.  3 * 10^{-13} 
B.  6 * 10^{-13} 
C.  4 * 10^{-10} 
D.  3 * 10^{-7} 
E.  3 * 10^{-1}

Question Discussion .

Example 1.6 (Difficulty: 505 Level)

If a certain machine produces bolts at a constant rate, how many seconds will it take the machine to produce 300 bolts?

(1) It takes the machine 56 seconds to produce 40 bolts.
(2) It takes the machine 1.4 seconds to produce 1 bolt.

Question Discussion .

Example 1.7 (Difficulty: 605 Level)

An actor read aloud and recorded a certain 420-page book on several audiotapes. Was the average recording time per page less than 90 seconds?

(1) Each tape was at most 40 minutes
(2) The book was recorded on 15 tapes

Question Discussion .

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Pattern #2: Multiple Entities Working Together   
 - Two or more workers collaborate on the task, combining their efforts.

Example 2.1 (Difficulty: 505 Level)

It would take 120 minutes for a leaky cold-water faucet to fill an empty bucket. It would take 200 minutes for a leaky hot-water faucet to fill the same bucket. How many minutes would it take both faucets, leaking at their respective constant rates, to fill the empty bucket if they began leaking into the bucket at the same time?

A. 60
B. 75
C. 90
D. 105
E. 160

Question Discussion .

Example 2.2 (Difficulty: 555 Level)

Eric can vacuum the carpeting in a particular office suite in 20 minutes. Ray can vacuum the the carpeting in the same office suite in 30 minutes. If they work together at their individual constant rates, how many minutes will they take to vacuum the carpeting in the office suite?

A. 10
B. 12
C. 24
D. 25
E. 30

Question Discussion .

Sharon and Ramla frequently mow their grandfather's yard. Working at her normal pace, Sharon can mow the yard in 5 hours. When Sharon and Ramla work together, each at her own normal pace, they can mow the yard in 3 hours. Yesterday, Ramla mowed the yard by herself. Given that Ramla was mowing at her normal pace, how long, in hours, did it take for Ramla to mow the yard?

A. 7
B. 7.5
C. 8
D. 8.5
E. 9

Question Discussion .

Machines J, K, and M, working together at their respective constant rates, produce c parts in 4 hours. Machine J, working alone at its constant rate, produces c parts in 10 hours, and machine K, working alone at its constant rate, produces c parts in 12 hours. How many hours does it take machine M, working alone at its constant rate, to produce c parts?

A. 11
B. 14
C. 15
D. 18
E. 20

Question Discussion .

Ed's own pump, operating alone at its constant rate, can empty his swimming pool in 15 hours. The pump Ed rented, operating alone at its constant rate, can empty his swimming pool in 5 hours. How many hours will it take the two pumps, operating simultaneously and independently at their respective constant rates, to empty Ed's pool?

A.  3 
B.  3 \frac{1}{4} 
C.  3 \frac{1}{2} 
D.  3 \frac{3}{4} 
E.  4

Question Discussion .

Working together at their respective constant rates, machine R, machine S, and machine T can produce a batch of parts in 4 hours. If machine R, working alone at its constant rate, can produce the same batch of parts in 6 hours, how many hours would it take machine S and machine T, working together at their respective constant rates, to produce the same batch of parts?

A. 6
B. 8
C. 10
D. 12
E. 14

Question Discussion .

Snowplow S, working alone at its own constant rate, will clear a certain parking lot in 6 hours. Snowplow S and snowplow T, working simultaneously and independently at their respective constant rates, will clear the parking lot in 2.4 hours. How many hours will it take snowplow T, working alone at its own constant rate, to clear the parking lot?

A. 3
B. 3.6
C. 4
D. 4.2
E. 4.4

Question Discussion .

Machine X caps 20 bottles of soda per minute, and machine Y caps 60 bottles of soda per minute. If both machines start operating at the same time and at their respective constant rates, in how many seconds will machine Y have capped 12 more bottles of soda than machine X?

A. 15
B. 18
C. 20
D. 21
E. 24

Question Discussion .

Medium PS:

When it operates at its own constant rate, hose A can fill an empty tank twice as fast as hose B can when it operates at its own constant rate. If hose A can fill the tank in x hours, how many hours will it take for the two hoses, operating simultaneously, to fill the tank?

A. 2x/3
B. 3x/2
C. 3x
D. 3/(2x)
E. 3/x

Question Discussion .

If machine X works alone at its constant rate, it fills a certain production order of bolts in 4 hours. If machine Y works alone at its constant rate, it fills the same production order in 6 hours. If the two machines work simultaneously and independently at their respective constant rates to fill this production order, what fraction of the number of bolts in the order will be made by machine X?

A. 1/3
B. 2/5
C. 5/12
D. 3/5
E. 2/3

Question Discussion .

Hard PS:

Candle A and Candle B have equal heights but different volumes. While the candles are burning, the height of each candle decreases at its own individual rate, with Candle A taking a total of t minutes to completely burn down and Candle B taking a total of 2t minutes to completely burn down. If both candles begin burning at the same time, in terms of t, how many minutes will it take for Candle B's height to be twice Candle A's height?

A. 1/4 t
B. 1/3 t
C. 2/3 t
D. 3/4 t
E. t

Question Discussion .

Medium DS:

Printing presses, Press A and Press B, are used to print the daily edition of a certain newspaper. Working together at their individual constant rates, how many hours did it take the 2 presses to print the daily edition of the newspaper yesterday?

(1) Yesterday, Press A printed newspapers at a rate of 4,000 newspapers per hour.
(2) Yesterday, Press B printed newspapers at 75% the rate that Press A printed.

Question Discussion .

A bank has 2 paper shedding machines, one large and one small, to shred sheets of secure waste paper, all of which are the same size. The large machine shreds sheets at a constant rate that is 5 times the constant rate of the small machine. How many minutes would it take the small machine, working alone at its constant shredding rate, to shred n sheets of the paper?

(1) Working together at their individual constant rates, the machines could shred n sheets of the paper in 40 minutes.

(2) n = 1,200

Question Discussion .

If two copying machines work simultaneously at their respective constant rates, how many copies do they produce in 5 minutes?

(1) One of the machines produces copies at the constant rate of 250 copies per minute.
(2) One of the machines produces copies at twice the constant rate of the other machine.

Question Discussion .

Hard DS:

Workers A, B, and C, working at their individual constant rates, can work together and complete a piece of work in 6 days. How long will it take for B and C alone to complete the work?

(1) A is twice as efficient as B. B is three times as efficient as C.
(2) The time taken by A to do 9 units of work is the same as the time taken by B and C together to do 6 units of work.

Question Discussion .

Machines P, Q, and R produce aluminum cans at their respective constant rates. Is machine P's rate greater than machine Q's rate?

(1) Machine P's rate is greater than machine R's rate.

(2) Machines P and R, working simultaneously, produce a total of 1,000 aluminum cans in half the time that it takes machine Q, working alone, to produce 1,000 aluminum cans.

Question Discussion .

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Pattern #3: Changing Workforce During the Task   
 - The number of workers changes mid-task—some may join late, leave early, or take breaks, altering the total work rate.

Medium PS:

Machine K and Machine N, working simultaneously and independently at their respective constant rates, process 2/3 of the shipment of a certain chemical product in 1.6 hours. Then machine K stopped working, and Machine N, working alone at it's constant rate, processed the rest of the shipment in 2 hours. How many hours would it have taken Machine K, working alone at it's constant rate, to process the entire shipment?

A. 3.8
B. 4.0
C. 4.8
D. 5.4
E. 6.0

Question Discussion .

Pump A, pumping water at a constant rate, can fill a certain swimming pool in 6 hours. Pump B, pumping water at a constant rate, can fill the same pool in 4 hours. If both pumps begin filling the pool simultaneously when the pool is empty and pump B breaks down 1 hour after they begin filling the pool, how many hours will it take pump A alone to finish filling the pool?

A. 1 2/5
B. 2 1/3
C. 3 1/2
D. 4
E. 4 4/5

Question Discussion .

﻿ https://gmatclub.com/forum/download/file.php?id=73559  
 The number of hours required for a certain company to produce 1 unit of products X, Y, and Z, respectively, are shown in the table. Products X and Y can be produced simultaneously, and so can products X and Z; but products Y and Z cannot be produced simultaneously. What is the least number of hours required to produce a total of 10 units of product X, 5 units of product Y, and 7 units of product Z?

A. 35
B. 45
C. 55
D. 65
E. 85

Question Discussion .

During each shift at a certain factory, nails are manufactured at a constant rate of 60 nails per 5 seconds and packaged at a constant rate of 100 nails per 9 seconds. If there are 1,000 nails that are not packaged at the start of a certain shift and if each shift lasts more than 2 hours, how many nails are there that are not packaged 2 hours after the start of the shift?

A. 2,000
B. 3,200
C. 4,500
D. 6,000
E. 7,400

Question Discussion .

Hard PS:

Machine H produces a certain product at a constant rate of 3 dozen units per hour, and machine K produces the same product at a constant rate of 4 dozen units per hour. The two machines produced 77 dozen units during a 14-hour period, and at least one of the two machines was working at any time in that period. What was the least amount of time that the two machines could have worked simultaneously in that period to complete the production of 77 dozen units?

A. 7 hr
B. 7 hr 30 min
C. 8 hr 45 min
D. 10 hr 15 min
E. 11 hr

Question Discussion .

Two machines, X and Y, working together at their respective constant rates for 14 hours, and then machine Y, working alone at its constant rate for an additional 4 hours, can produce a total of m items. The time that it takes machine X, working alone at its constant rate, to produce m items is 8 hours less than the time that it takes machine Y, working alone at its constant rate, to produce m items. How many hours does it take machine Y, working alone at its constant rate, to produce m items?

A. 28
B. 30
C. 32
D. 34
E. 36

Question Discussion .

Hard DS:

If Machine X, working alone at its constant rate, performs half of a certain task and then Machine Y, working alone at its constant rate, performs the rest of the task, the whole task will take a total of 16 hours. How many hours will it take machine X, working alone at its constant rate, to perform the task?

(1) Working together at their respective constant rates, machines X and Y perform the task in 6 hours.

(2) Machine X has a faster rate than machine Y.

Question Discussion .

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Pattern #4: Opposing Work Rates (Negative Rates)   
 - Some elements hinder progress, such as leaks, drains, or counteracting forces, effectively reducing the net work rate.

Hard PS:

Throughout last week, water was leaking from a certain tank at a constant rate of  \frac{1}{4}  gallon per hour, and 14 gallons of water were added to the tank every day at 1 o'clock in the afternoon. If there were  32 \frac{3}{4}  gallons of water in the tank at 2 o'clock last Tuesday afternoon, at what time last week were there  46 \frac{3}{4}  gallons of water in the tank?

A. 2 o'clock Wednesday afternoon
B. 1 o'clock Thursday morning
C. 6 o'clock Thursday morning
D. 10 o'clock Thursday evening
E. 2 o'clock Friday morning

Question Discussion .

Medium DS:

Pipes A and B are the pipes that fill a tank. Pipes C and D are the pipes that empty the same tank. What is the capacity of the tank?

(1) Pipe A is twice as efficient as Pipe C, that is, the volume of water per hour that Pipe A moves is twice the volume per hour that Pipe C moves. Pipe A and Pipe B are equally efficient. When Pipes C and D are closed, Pipes A and B together fill the empty tank in 5 hours. Pipe C empties 6,000 liters per hour.
(2) Pipe B is three times as efficient as Pipe D.

Question Discussion .

___________________________________________

Theory:

•  Work Rate Problems - All in One Topic! 
•  Work Word Problems Made Easy 
•  How to Solve Relative Rate of Work Questions on the GMAT

Questions:

•  Problem Solving - HARD Work and Rate Questions 
•  Problem Solving - MEDIUM Work and Rate Questions 
•  Problem Solving - EASY Work and Rate Questions

•  Data Sufficiency - HARD Work and Rate Questions 
•  Data Sufficiency - MEDIUM Work and Rate Questions 
•  Data Sufficiency - EASY Work and Rate Questions

Bunuel · Accepted Answer

Here’s what we have so far:

GMAT Question Patterns: Work and Rate Problems  
  GMAT Question Patterns: Arithmetic  
  GMAT Question Patterns: Absolute Value  
  GMAT Question Patterns: Distance and Speed  
  GMAT Question Patterns: Remainders  
  GMAT Question Patterns: Algebra  
  GMAT Question Patterns: Overlapping Sets  
  GMAT Question Patterns: Sequences

We’ll be adding other patterns gradually, including those on divisibility, overlapping sets, and sequences.

NEYR0N · Answer

Thank you for this,  Bunuel

Is there maybe a set of questions with recurring patterns involving:

1) divisibility 
2) overlapping sets
3) Weighted averages
3) progressions 
for GMAT FOCUS 2024-2025?

NextstopISB · Answer

Hi Bunuel this is really helpful, do we have same thing for Verbal and DI?

Bunuel · Answer

_______________
No, not yet.

Bunuel · Answer

GMAT Question Patterns:

GMAT Question Patterns: Work and Rate Problems  
  GMAT Question Patterns: Arithmetic  
  GMAT Question Patterns: Absolute Value  
  GMAT Question Patterns: Distance and Speed  
  GMAT Question Patterns: Remainders  
  GMAT Question Patterns: Algebra  
  GMAT Question Patterns: Overlapping Sets

SIDDHANT1122 · Answer

Thanks a ton for this Bunuel! Appreciate the hardwork you've put in. I just have 3 qs
What all topics would you be covering next? And by when would you cover the complete syllabus? Would it be suffient for me to just go through these patterns and practice just these to get a perfect score in quant?

Bunuel · Answer

Haven’t decided yet. Any suggestions? 
 We’ll be publishing one pattern per week, so it will take some time to cover everything. 
 It depends on your current level. These patterns are very helpful, but for a perfect score in quant, you’d still need additional practice and review beyond just these.

SIDDHANT1122 · Answer

Since you mentioned you're already working on divisibility and sequences id suggest 
1) Fractions Ratio and Percentages 
2) mixture allegation 
3) probability 
4) Inequalities and Min max type
5) Coordinate geometry and graphs and illustrations 
6) powers and exponents

Bunuel · Answer

Thank you. Will keep in mind.

Bunuel · Answer

New one:  GMAT Question Patterns: Sequences

rak08 · Answer

link for 1.5 - arithmetic operations please fix  Bunuel

Bunuel · Answer

Fixed the link. Thank you!

Bunuel · Answer

The new pattern topic:  GMAT Question Patterns: Functions and Custom Characters .

SIDDHANT1122 · Answer

Are you going to be adding anything new? Havent see anything lately

andrear0driguez · Answer

Are there sets that aren't GMAT Prep (focus) since all of the focus questions tend to show up on the mocks and I don't want to ruin my mocks.

Bunuel · Answer

Some questions come from official mocks, so pay attention to the tags when practicing, or ignore those questions altogether.

GMAT Question Patterns: Work and Rate Problems

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