Work rate problems
49 flashcards covering Work rate problems for the GMAT Quantitative section.
Work rate problems deal with how quickly people, machines, or teams complete tasks, often involving rates of work over time. For instance, if one person can paint a house in 4 hours and another in 6 hours, these problems help determine how long it would take them working together. At their core, they use simple math to combine individual rates, expressed as fractions of a job per unit of time, to solve for unknowns like total time or combined effort.
On the GMAT Quantitative section, work rate questions appear as word problems that test your ability to set up equations and manipulate rates, often in scenarios involving pipes filling tanks or workers on assembly lines. Common traps include adding times instead of rates or overlooking overlapping work, so focus on converting everything to consistent units and using the formula: work = rate × time. A solid grasp of these concepts can boost your accuracy on timing-sensitive questions.
Always add individual rates to find the combined rate.
Terms (49)
- 01
Work Rate
Work rate is the amount of work done per unit of time, typically expressed as a fraction of a job completed per hour.
- 02
Formula for Work Rate
The formula for work rate is Rate equals Work divided by Time, where work is often 1 complete job and time is in hours.
- 03
Time to Complete Work
Time to complete a job is calculated by dividing the total work by the work rate, such as Time equals 1 job divided by the rate.
- 04
Combined Work Rates
Combined work rates occur when multiple entities work together, adding their individual rates to find the total rate for the job.
- 05
Adding Rates for Same Direction
When two or more workers perform the same task, their rates are added together to determine the combined rate.
- 06
Subtracting Rates for Opposite Directions
In problems like pipes filling and emptying a tank, subtract the rate of the entity working against the task from the rate working for it.
- 07
Reciprocal of Time as Rate
The work rate can be found as the reciprocal of the time taken to complete one job, such as Rate equals 1 divided by Time.
- 08
Inverse Relationship in Work
In work problems, the time taken is inversely proportional to the number of workers, meaning more workers reduce the time proportionally.
- 09
Work Done by Multiple Workers
To find total work done, multiply the combined rate by the time worked, ensuring all rates are in the same units.
- 10
Efficiency in Work Problems
Efficiency measures how quickly a worker completes a job compared to others, often as a ratio of their rates.
- 11
Pipes and Cistern Problems
These involve rates of pipes filling or emptying tanks, requiring addition or subtraction of rates to find net filling or emptying time.
- 12
Least Common Multiple in Cycles
Use the least common multiple when workers have different work cycles to determine when they complete tasks simultaneously.
- 13
Common Trap: Adding Times
A frequent error is adding the times taken by individual workers instead of adding their rates when they work together.
- 14
Example: One Worker
If a worker completes a job in 4 hours, their rate is 1/4 job per hour, so for 2 jobs, it takes 8 hours.
A painter finishes one house in 4 hours, so two houses take 8 hours.
- 15
Example: Two Workers Together
If Worker A takes 3 hours and Worker B takes 6 hours alone, together their combined rate is 1/3 + 1/6 = 1/2 job per hour, so they finish in 2 hours.
- 16
Example: Different Worker Rates
If one worker's rate is 2 jobs per day and another's is 3 jobs per day, together they do 5 jobs per day.
- 17
Workers Starting at Different Times
Calculate the effective time by considering how long each worker is active, then use combined rates for the overlapping period.
- 18
Worker A Then Worker B
If Worker A works for some time then Worker B takes over, add the work done by each based on their individual rates and times.
- 19
Fractional Work Completion
Work can be a fraction of a job, so if a worker's rate is 1/5 job per hour, in 2 hours they complete 2/5 of the job.
- 20
Rate in Jobs per Hour
Express rates consistently in jobs per hour to avoid errors, converting from other units like per day as needed.
- 21
Converting Time Units
Always convert time units to match, such as from minutes to hours, before calculating combined rates.
- 22
Solving for Unknown Rate
Set up an equation using the work formula; for example, if two workers together take 2 hours, solve for one rate given the other.
- 23
Algebraic Setup for Work
Use variables for unknown rates or times and set up equations based on total work equaling 1 job.
- 24
Identifying Rates from Words
In word problems, rates are often given as time to complete a job, which you convert to a rate by taking the reciprocal.
- 25
Pitfall: Assuming Equal Sharing
Do not assume workers share work equally; base calculations on their actual rates.
- 26
Variable Work Rates
Some problems involve rates that change, requiring you to break the problem into segments with constant rates.
- 27
Men and Women Working
Treat workers as having different rates based on their described efficiencies, then combine as needed.
- 28
Machines with Different Speeds
Machines have rates like parts assembled per hour, and you add or subtract based on whether they assist or hinder.
- 29
Overtime in Work Problems
Account for overtime by adjusting the time period in which a worker operates at their rate.
- 30
Minimum Time for Task
To minimize time, maximize the combined rate by using the fastest workers or machines.
- 31
Work Rate with Breaks
If workers take breaks, subtract the break time from the total time when calculating effective work done.
- 32
Proportional Rates
Rates can be proportional to the number of workers, but verify if the problem states this explicitly.
- 33
Net Rate Calculation
Net rate is the difference between positive and negative rates, used in scenarios like inflow and outflow.
- 34
Example: Three Workers
If three workers have rates of 1/2, 1/3, and 1/6 job per hour, together they complete a job in 1 divided by (1/2 + 1/3 + 1/6) hours, which is 1 hour.
- 35
Daily vs. Hourly Rates
Convert daily rates to hourly by dividing by the number of hours worked per day for consistency.
- 36
Strategy for Rate Equations
Set up equations where total work equals the sum of work done by each entity over time.
- 37
Common Trap: Unit Mismatch
Ensure all rates use the same time units to avoid incorrect additions or subtractions.
- 38
Inverse Variation Formula
Time is inversely proportional to rate, so Time1 times Rate1 equals Time2 times Rate2 for the same work.
- 39
Partial Job Scenarios
In some problems, workers stop after completing a fraction of the job, requiring partial rate calculations.
- 40
Example: Pipe Filling Tank
If Pipe A fills a tank in 4 hours and Pipe B in 6 hours, together they fill it in 1 divided by (1/4 + 1/6) hours, about 2.4 hours.
Two pipes fill a 100-gallon tank in roughly 2.4 hours together.
- 41
Rate Comparison
Compare rates to determine who is faster or how long it takes for one to catch up in work.
- 42
Work Rate Graphs
Though rare, graphs might show work progress over time, requiring you to interpret slopes as rates.
- 43
Efficiency Ratios
An efficiency ratio compares actual rate to a standard, helping in problems with varying worker speeds.
- 44
Strategy for Optimization
To optimize work completion, calculate which combination of workers minimizes total time.
- 45
Example: Workers with Overlap
If Worker A works 2 hours alone then Worker B joins, calculate work done in each phase and sum to 1 job.
- 46
Negative Rates
Rates can be negative for tasks that undo work, like a leak in a tank.
- 47
Total Man-Hours
Total man-hours is the product of number of workers and time, useful for verifying work amounts.
- 48
Pitfall: Ignoring Dependencies
Do not overlook if one worker's task depends on another's completion.
- 49
Advanced: Simultaneous Equations
Set up multiple equations for problems with several unknowns, like rates and times.