The GRE Quantitative Reasoning section frequently features rate and work problems—questions that combine math concepts with real-world problem-solving. These can be intimidating at first, but with the right framework and plenty of practice, you’ll learn to approach them with confidence and accuracy.
What Are Rate and Work Problems?
Rate and work problems involve calculating the speed or efficiency at which a task is completed. This might involve how quickly a job can be done, how long two people working together take to complete a task, or how changing variables like time or effort impact outcomes. These problems are common in fields like business, engineering, logistics, and economics—making them valuable both on and beyond the GRE.
The key formula to remember is:
Work = Rate × Time
This formula serves as the foundation for solving nearly all rate and work problems. Let’s break down a common example using a four-step approach.
Step 1: Understand the Problem
Start by reading carefully and identifying the knowns and unknowns. Pay close attention to what’s being asked and underline key values or phrases.
Example: “John can complete a project in 10 days, while his colleague Mark can finish the same project in 15 days. How long will it take for them to complete the project if they work together?”
You’re being asked for the time it takes both to complete the task together. John’s rate is 1 project per 10 days (1/10), and Mark’s is 1 project per 15 days (1/15).
Step 2: Set Up the Equation
We apply the formula using a combined rate approach:
(1/10) × t + (1/15) × t = 1
This equation represents the total amount of work done (1 full project) when both John and Mark contribute simultaneously.
Step 3: Solve the Equation
Combine the rates and solve for t:
(1/10 + 1/15)t = 1
Find the least common denominator (LCD of 10 and 15 is 30):
(3/30 + 2/30)t = 1 → (5/30)t = 1
Simplify:
(1/6)t = 1 → t = 6
Answer: It will take them 6 days to finish the project together.
Step 4: Double-Check Your Work
Always verify your solution by plugging it back into the original equation:
(1/10 × 6) + (1/15 × 6) = 0.6 + 0.4 = 1
The equation holds true—your answer is correct!
Practice Makes Perfect
Rate and work problems are formulaic, but accuracy comes from repetition. Here are a few trusted resources to practice:
Final Thoughts
Rate and work problems are among the most manageable GRE Quant questions—once you master the strategy. Remember:
- Read carefully to extract key data
- Set up a clear equation using rate × time = work
- Solve methodically with algebraic precision
- Always double-check your solution
Approach these questions not with fear, but as a chance to demonstrate your quantitative logic. With consistent practice, you’ll not only improve your score but also build problem-solving skills that carry into your career.
Good luck—and happy studying!