The Formula Triangle
All speed, distance and time problems use one of three related formulas:
The SDT Triangle
Cover the value you want to find — the remaining two show you what to do:
- Cover D → S × T
- Cover S → D ÷ T
- Cover T → D ÷ S
Key rule: Speed, distance and time must all use consistent units. If speed is in km/h, distance must be in km and time in hours.
Unit Conversions
Many exam questions mix units on purpose. Always convert before applying the formula.
Time: Hours ↔ Minutes
| To convert | Operation | Example |
|---|
| Hours → Minutes | × 60 | 1.5 h = 90 min |
| Minutes → Hours | ÷ 60 | 45 min = 0.75 h |
Speed: km/h ↔ m/s
| To convert | Operation | Example |
|---|
| km/h → m/s | ÷ 3.6 | 72 km/h = 20 m/s |
| m/s → km/h | × 3.6 | 25 m/s = 90 km/h |
Why 3.6? Because 1 km/h = 1000 m ÷ 3600 s = 1/3.6 m/s.
Quick check: m/s values are always much smaller than km/h values (roughly 3.6× smaller). If your answer looks unexpectedly large or small, you may have converted the wrong way.
Easy Examples
These problems use the formula directly — no unit conversion needed.
Example 1 — Find Distance
A car travels at a constant speed of 60 km/h for 3 hours. How far does it travel?
1Identify what you know: S = 60 km/h, T = 3 h, find D
2Use D = S × T
3D = 60 × 3 = 180 km
Example 2 — Find Speed
A cyclist covers 40 km in 2 hours. What is their average speed?
1Identify: D = 40 km, T = 2 h, find S
2Use S = D ÷ T
3S = 40 ÷ 2 = 20 km/h
Example 3 — Find Time
A runner jogs at 8 km/h. How long does it take to run 12 km?
1Identify: S = 8 km/h, D = 12 km, find T
2Use T = D ÷ S
3T = 12 ÷ 8 = 1.5 hours = 1 hour 30 minutes
Medium Examples
These problems require a unit conversion step before or after applying the formula.
Example 1 — Answer in Minutes
A train travels at a constant speed of 90 km/h. How many minutes will it take to cover 60 km?
1Identify: S = 90 km/h, D = 60 km, find T in minutes
2T = D ÷ S = 60 ÷ 90 = 2/3 hours
3Convert to minutes: 2/3 × 60 = 40 minutes
Example 2 — Time Given in Minutes
A bus covers 30 km in 45 minutes. What is its average speed in km/h?
1Convert time to hours: 45 min ÷ 60 = 0.75 h
2S = D ÷ T = 30 ÷ 0.75
3S = 40 km/h
Example 3 — Speed in m/s
A sprinter runs 100 metres in 10 seconds. What is their speed in km/h?
1S = D ÷ T = 100 ÷ 10 = 10 m/s
2Convert to km/h: 10 × 3.6 = 36 km/h
Strategy: Always write down what you know and what units the answer needs to be in before calculating. That prevents unit errors.
Complex Examples
These problems combine multiple steps, involve two objects, or require the average speed formula.
Example 1 — Two Objects Moving Apart
Two cars start from the same point and travel in opposite directions. Car A travels at 60 km/h and Car B at 80 km/h. How far apart are they after 2.5 hours?
1Moving apart → add speeds. Combined speed = 60 + 80 = 140 km/h
2D = S × T = 140 × 2.5 = 350 km
Example 2 — Two Objects Moving Towards Each Other
Two trains are 450 km apart and travel towards each other. Train A travels at 90 km/h and Train B at 60 km/h. When do they meet?
1Moving towards each other → add speeds. Combined speed = 90 + 60 = 150 km/h
2T = D ÷ S = 450 ÷ 150 = 3 hours
Example 3 — Average Speed (Equal Distances / Round Trip)
A person walks from A to B at 4 km/h and returns at 6 km/h. What is their average speed for the whole journey?
1The distance each way is equal, so use the harmonic mean: Avg S = 2 × S₁ × S₂ ÷ (S₁ + S₂). It is not the simple average of the two speeds.
2Avg S = 2 × 4 × 6 ÷ (4 + 6) = 48 ÷ 10 = 4.8 km/h
Why? Let distance A→B = d km. Time A→B = d/4 h, time B→A = d/6 h. Total distance = 2d. Total time = d/4 + d/6 = 5d/12. Avg S = 2d ÷ (5d/12) = 24/5 = 4.8 km/h.
Average Speed — Which Formula?
Average speed is always total distance ÷ total time. Depending on what is kept equal between the two legs, it simplifies:
| Situation | Formula |
|---|
Distances equal
e.g. there & back on the same route | Avg S = 2 × S₁ × S₂ ÷ (S₁ + S₂)
harmonic mean |
Times equal
each leg lasts the same time | Avg S = (S₁ + S₂) ÷ 2
simple average |
| Both different | Avg S = Total distance ÷ Total time |
Example 4 — Average Speed (Equal Times)
A driver travels at 30 km/h for 2 hours, then at 50 km/h for 2 hours. What is the average speed for the whole trip?
1The two legs take the same time, so use the simple average: Avg S = (S₁ + S₂) ÷ 2
2Avg S = (30 + 50) ÷ 2 = 40 km/h
Check: distance = 30×2 + 50×2 = 160 km, total time = 4 h, so 160 ÷ 4 = 40 km/h ✓
Example 5 — Average Speed (Distance & Time Both Different)
A cyclist rides 60 km at 20 km/h, then 30 km at 15 km/h. What is the average speed for the whole journey?
1Neither the distances nor the times match, so fall back to the definition: Avg S = Total distance ÷ Total time
2Time for leg 1 = 60 ÷ 20 = 3 h | Time for leg 2 = 30 ÷ 15 = 2 h
3Total distance = 60 + 30 = 90 km | Total time = 3 + 2 = 5 h
4Avg S = 90 ÷ 5 = 18 km/h
Example 6 — Train Passing a Point
A train 400 m long passes a stationary signal post in 20 seconds. Find the train's speed in km/h.
1Distance covered = length of train = 400 m
2S = D ÷ T = 400 ÷ 20 = 20 m/s
3Convert: 20 × 3.6 = 72 km/h
Common trap: You can only take the simple average of two speeds when the times are equal. When the distances are equal (e.g. a round trip), use the harmonic mean 2·S₁·S₂ ÷ (S₁ + S₂). When in doubt, always fall back to total distance ÷ total time — that works in every case.