How to Solve Speed Ratio and Time Ratio Problems
Learn the inverse-proportion shortcut for speed ratio and time ratio aptitude problems, with a worked example and practice questions.
Expected Interview Answer
For a fixed distance, speed and time are inversely proportional, so if two speeds are in ratio a:b, the corresponding times taken are in the inverted ratio b:a.
This inverse relationship follows directly from Distance = Speed × Time: since distance is constant, a larger speed must be paired with a proportionally smaller time to keep the product the same. If speeds are in ratio 3:5, times are in ratio 5:3 — the faster traveler (ratio 5) takes the smaller time share (ratio 3). This lets many ratio-based problems skip explicit distance and speed values entirely, working purely with the ratio numbers and one known time or time difference to find everything else. When a problem states a time difference (e.g., "the faster one arrives 20 minutes earlier"), that difference maps onto the gap between the ratio’s inverted terms, letting a single unit-value be solved for and then scaled up.
- Skips full speed/distance values — pure ratio manipulation solves most cases
- Inverting the speed ratio directly gives the time ratio without extra formulas
- A stated time difference pins down the actual unit value behind the ratio
- Same inverse-proportion logic applies to any two other inversely-related quantities
AI Mentor Explanation
Two bowlers with run-up speeds in the ratio 3:4 covering the identical run-up distance will take times in the inverted ratio 4:3 — the faster bowler, with the larger speed ratio number, needs the smaller time ratio number to cover the same ground. If the actual time difference between them is known, say the slower bowler takes 2 seconds longer, that 2-second gap corresponds to the '1 part' difference between ratio terms 4 and 3, letting you find the value of one ratio unit and then both actual times. This inverse-ratio trick avoids ever needing the actual run-up distance.
Worked example
Speed ratio
- 3 : 4
Time ratio (inverted)
- 4 : 3
Given gap = 20 min (1 unit)
- Times = 80 min, 60 min
Step-by-Step Explanation
Step 1
Confirm distance is fixed
The inverse-ratio rule only applies when both parties cover the same distance.
Step 2
Invert the speed ratio
Speed ratio a:b becomes time ratio b:a.
Step 3
Map the given time difference
A stated time gap equals the difference between the inverted ratio’s terms, in ratio-unit terms.
Step 4
Solve for one unit and scale up
Divide the given difference by the ratio-term gap to get one unit’s value, then multiply out both actual times.
What Interviewer Expects
- Correct inversion of speed ratio to time ratio for fixed distance
- Recognizing that a stated time difference maps to the ratio-term gap
- Solving for one ratio unit before scaling to find actual times
- Awareness that the inverse relationship requires distance to be constant
Common Mistakes
- Keeping the speed ratio unchanged instead of inverting it for time
- Applying the inverse-ratio shortcut when distances are actually different
- Misassigning which ratio term corresponds to the faster vs slower party
- Failing to convert the final ratio units into an explicit time value using the given difference
Best Answer (HR Friendly)
“For the same distance, speed and time move in opposite directions, so a speed ratio simply flips to become the time ratio — three to four in speed becomes four to three in time. Whenever the problem also gives an actual time difference, that difference matches the gap between the ratio’s two numbers, which lets you find what one ratio unit is worth in minutes and then scale both times up from there.”
Follow-up Questions
- Why does the inverse-ratio rule fail if the two parties travel different distances?
- How would you extend this to three parties with a given speed ratio?
- How does this connect to the general D = S × T relationship?
- What if the problem gives a distance difference instead of a time difference?
MCQ Practice
1. Two trains have speeds in the ratio 5:7 over the same distance. Their times taken are in the ratio?
Speed and time are inversely proportional for the same distance, so the ratio inverts to 7:5.
2. Two cars have speeds in ratio 2:3 for the same distance. If the slower car takes 30 minutes more, the faster car’s time is?
Time ratio (inverted from speed 2:3) is 3:2. The 1-unit gap between ratio terms equals 30 minutes, so times are 90 minutes (slower, ratio 3) and 60 minutes (faster, ratio 2).
3. If speed ratio of A to B is 1:2 for the same distance, time ratio of A to B is?
Inverting the speed ratio 1:2 gives time ratio 2:1.
Flash Cards
Relationship between speed ratio and time ratio for fixed distance? — They are inverses of each other: speed ratio a:b gives time ratio b:a.
Why does the ratio invert? — Distance = Speed × Time is constant, so speed and time are inversely proportional.
How to use a given time difference in a ratio problem? — Map it to the difference between the inverted ratio’s terms to find the value of one unit.
When does the inverse-ratio rule fail? — When the two parties do not travel the same fixed distance.