How to Solve Time, Speed and Distance Problems
Solve time, speed and distance aptitude problems — the core formula, unit conversion, average and relative speed — with a worked example and practice questions.
Expected Interview Answer
Time, speed and distance problems all reduce to one relation: Distance = Speed × Time, rearranged as Speed = Distance ÷ Time or Time = Distance ÷ Speed, with consistent units.
Keep units consistent — convert km/h to m/s by multiplying by 5/18, and m/s to km/h by 18/5. When speed is constant, distance and time are directly proportional; over a fixed distance, speed and time are inversely proportional. Average speed for equal distances is the harmonic mean (2ab/(a+b)), not the arithmetic mean. Relative speed adds for opposite directions and subtracts for the same direction.
- One formula underlies every variation
- Unit conversion (5/18, 18/5) prevents errors
- Relative-speed rules solve trains/boats problems
AI Mentor Explanation
A delivery’s speed is just distance over time: the ball covers ~20 metres from hand to bat, and dividing that distance by the time gives the speed the radar shows. Bowl the same distance faster and the time shrinks — speed and time are inversely related over a fixed distance. Every time-speed-distance problem rests on this single relation: Distance = Speed × Time, rearranged as needed.
Worked example
Distance
- 300 km
Speed
- 60 km/h
Time
- 300 ÷ 60 = 5 h
Step-by-Step Explanation
Step 1
Use the core relation
Distance = Speed × Time; rearrange for the unknown.
Step 2
Fix the units
km/h → m/s via ×5/18; m/s → km/h via ×18/5.
Step 3
Proportionality
Fixed speed: distance ∝ time. Fixed distance: speed ∝ 1/time.
Step 4
Average & relative speed
Equal distances → harmonic mean; opposite directions add, same direction subtract.
What Interviewer Expects
- The Distance = Speed × Time relation and rearrangements
- km/h ↔ m/s conversion factors (5/18, 18/5)
- Harmonic mean for average speed over equal distances
- Relative speed for trains/boats problems
Common Mistakes
- Using the arithmetic mean for average speed
- Mixing units (km/h with metres/seconds)
- Adding instead of subtracting relative speed for same direction
- Forgetting time and speed are inversely related over fixed distance
Best Answer (HR Friendly)
“Everything comes from Distance = Speed × Time. Rearrange it for whatever you need, and keep units consistent — convert km/h to m/s by multiplying by 5/18. Remember that for a round trip at two speeds, the average speed is the harmonic mean, not the simple average.”
Code Example
def time_taken(distance, speed):
return distance / speed
print(time_taken(300, 60)) # 5.0 hours
# average speed over equal distances (harmonic mean)
def avg_speed(a, b):
return 2 * a * b / (a + b)
print(avg_speed(60, 40)) # 48.0 km/h, not 50Follow-up Questions
- Why is average speed the harmonic mean for equal distances?
- How do you compute relative speed for two trains?
- How do boats-and-streams problems use speed?
- How do you convert 72 km/h to m/s?
MCQ Practice
1. A car travels 150 km in 2.5 hours. Its speed is?
Speed = Distance ÷ Time = 150 ÷ 2.5 = 60 km/h.
2. 36 km/h in m/s is?
Multiply by 5/18: 36 × 5/18 = 10 m/s.
3. Average speed over equal distances at 60 and 40 km/h is?
Harmonic mean = 2×60×40/(60+40) = 4800/100 = 48 km/h.
Flash Cards
Core relation? — Distance = Speed × Time.
km/h to m/s? — Multiply by 5/18.
Average speed (equal distances)? — Harmonic mean: 2ab/(a+b), not the arithmetic mean.
Relative speed? — Add for opposite directions, subtract for the same direction.