Speed, Time, and Distance (TSD) questions are a cornerstone of GMAT Quantitative Reasoning and Data Insights. Beyond basic calculation (Distance = Speed × Time), the GMAT tests your mastery of algebraic rate expressions, average speed weighted logic, relative motion (catch-up and collision scenarios), and Data Sufficiency rephrasing.
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 the crucial difference between simple average of speeds and the correct "Total Distance / Total Time" formula for complex journeys.
Car travels A to B at 40 km/hr.
Returns B to A at 60 km/hr.
What is the average speed?
Master the two core scenarios for relative speed (objects moving in opposite vs. same directions) using a visual race simulator.
A (2 m/s) and B (3 m/s) are 100m apart.
Apply relative speed concepts to the classic GMAT problem types involving trains crossing platforms, boats in streams, and escalators.
Apply interactive Data Sufficiency strategies to TSD. Learn how to rephrase question stems, evaluate weighted sums directly, and compare meeting point proximity.
Look for the combined algebraic expression (2x + 3y) rather than solving for individual variables x and y.
Marta's Average Speed
Marta averaged x mph for 2 hours and y mph for the remaining 3 hours. What was her average speed, in miles per hour, for the entire trip?
(1) 2x + 3y = 280
(2) y = x + 10
Total Distance = 2x + 3y
Total Time = 2 + 3 = 5 hours
Strategic Rephrase: We only need the exact value of the expression (2x + 3y) to find the answer.
Substitute 280 directly into our target expression:
A unique numerical value is obtained → SUFFICIENT.
Substitute y into our target expression:
Since x is unknown, the average speed can vary → INSUFFICIENT.
Final Answer: (A)
A dedicated question set for Speed, Time & Distance is currently being authored. In the meantime, test your baseline score on the full Diagnostic:
Don't just solve questions sequentially. Learn the error log method and how to use the OG for maximum score gains.
Stop calculating! Learn how to use the properties of symmetry to solve hard SD questions in seconds.
Stop calculating sums! Learn the 'Average of First & Last' rule to solve Arithmetic Progression (AP) problems in seconds.