Rate and motion problems on the GRE Quant section test your conceptual grasp of proportionality, relative speed, and weighted averages. By mastering core frameworks and Quantitative Comparison shortcuts, you can bypass tedious calculations and solve rate questions with speed and confidence.
Master the fundamental Distance = Speed × Time relationship, explore the 3 algebraic rearrangements, and practice instant unit conversions with our interactive tool.
All motion questions test the relationship between three variables: Distance, Speed (Rate), and Time.
Distance = Speed × Time
Speed = Distance / Time
Time = Distance / Speed
Master inverse variation (constant distance) and direct variation (constant time) with step-by-step interactive problem models.
When distance is constant, Speed and Time are inversely proportional.
If speed is multiplied by k, time required becomes 1/k.
Carl and Ruth
Carl averaged 2m mph on a trip that took him h hours.
If Ruth made the same trip in (2/3)h hours, what was her average speed in mph?
Step A: Find the total distance.
Step B: Divide distance by Ruth's time.
Notice that variable h cancels out cleanly.
Principle: For constant distance, the speed ratio is the inverse of the time ratio:
Step A: Compare their times.
Ruth's time is 2/3 of Carl's time (ratio of Carl's time to Ruth's time is 3 : 2).
Step B: Invert the ratio for speed.
Since speed is inversely proportional to time, Ruth's speed must be 3/2 of Carl's speed:
Why use the Ratio Shortcut?
The algebraic method requires setting up and simplifying compound algebraic fractions. The ratio shortcut lets you solve it in 5 seconds mentally: Time scaled by 2/3 → Speed scaled by 3/2 → (3/2) × 2m = 3m.
Learn why simple averages fail for round trips and how to apply the true Total Distance / Total Time framework seamlessly.
Car travels A to B at 40 km/hr.
Returns B to A at 60 km/hr.
What is the average speed?
Understand the physics of opposite-direction closing speeds vs. same-direction overtaking speeds with our dynamic simulator.
A (2 m/s) and B (3 m/s) are 100m apart.
Step-by-step breakdowns for train platform crossings, upstream/downstream river currents, and escalator problems.
Bypass tedious formulas on QC questions by using speed weighting logic and speed-distance ratios to compare quantities instantly.
On GRE Quantitative Comparison, you can determine whether average speed is greater or less than the midpoint without computing any exact numbers.
A motorist travels from Town A to Town B at 40 mph and returns along the same route from Town B to Town A at 60 mph.
Assume distance between Town A and B = 120 miles (LCM of 40 and 60):
Since 48 mph < 50 mph → Quantity B is greater (takes 45–60 seconds).
Why is the average speed always pulled below 50 mph?
Average speed is a time-weighted average, not a simple average of numbers:
Correct Answer: (B)
A dedicated question set for Speed, Time & Distance is currently being authored. In the meantime, test your baseline score on the full Diagnostic:
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