The time formula is derived from the speed-distance-time relationship: $\text{Time} = \dfrac{\text{Distance}}{\text{Speed}}$.
Quick Reference — Time Formula
Time formula: $T = \dfrac{D}{S}$
Speed formula: $S = \dfrac{D}{T}$
Distance formula: $D = S \times T$
Units: Time in hours (h), minutes (min), or seconds (s); Distance in km, m, miles; Speed in km/h, m/s, mph
Conversion: $1 \text{ km/h} = \dfrac{5}{18} \text{ m/s}$; $1 \text{ m/s} = \dfrac{18}{5} \text{ km/h}$
Type: Arithmetic formula — kinematics / mensuration
Used in: Physics, everyday travel, competitive mathematics, Class 7–10 curricula
Definition
The three quantities — speed ($S$), distance ($D$), and time ($T$) — are related by the single equation $D = S \times T$. Each quantity can be found when the other two are known:
$$T = \frac{D}{S} \qquad S = \frac{D}{T} \qquad D = S \times T$$
Speed is the rate at which distance is covered per unit time. Time is how long the journey takes. Distance is how far was travelled.
The Speed-Distance-Time Triangle
The triangle is a memory device. Cover the quantity you want to find; the remaining two show what to do — multiply if side by side, divide if one is above the other.
Cover D: $D = S \times T$
Cover S: $S = D \div T$
Cover T: $T = D \div S$
Unit Conversions
Speed units must match distance and time units before substituting into the time formula.
$$1 \text{ km/h} = \frac{5}{18} \text{ m/s}$$
$$1 \text{ m/s} = \frac{18}{5} \text{ km/h} = 3.6 \text{ km/h}$$
If distance is in km and time is needed in minutes, convert: time in hours $\times$ 60 = time in minutes.
Variable Key
Symbol | Meaning | Common units |
|---|---|---|
$D$ | Distance | km, m, miles |
$S$ | Speed (uniform/average) | km/h, m/s, mph |
$T$ | Time | h, min, s |
Worked Examples of Time Formula
Example 1: Finding time
A car travels 240 km at a speed of 80 km/h. How long does the journey take?
$$T = \frac{D}{S} = \frac{240}{80} = 3 \text{ hours}$$
Final answer: 3 hours
Example 2: Finding speed
A train covers 540 km in 4.5 hours. Find its average speed.
$$S = \frac{D}{T} = \frac{540}{4.5} = 120 \text{ km/h}$$
Final answer: 120 km/h
Example 3: Converting units then finding time
A cyclist rides at 10 m/s. How long (in minutes) does it take to cover 3 km?
Convert distance to metres: $3 \text{ km} = 3000 \text{ m}$.
$$T = \frac{D}{S} = \frac{3000}{10} = 300 \text{ s} = 5 \text{ minutes}$$
Final answer: 5 minutes
Origin
The relationship $D = S \times T$ formalises the intuitive notion that covering more distance at the same speed takes more time. Galileo Galilei (1564–1642, Italy) was among the first to study uniform and accelerated motion systematically in Two New Sciences (1638), establishing the quantitative link between distance, speed, and time that forms the basis of classical kinematics.
Common confusions wWth The Time Formula
Units must match throughout the calculation. Speed in km/h with distance in metres gives a time in the wrong unit — always align units before substituting.
Average speed is not the same as the mean of two speeds. If a car travels half a journey at 40 km/h and the other half at 60 km/h, the average speed is $\frac{2 \times 40 \times 60}{40 + 60} = 48$ km/h — the harmonic mean, not $\frac{40+60}{2} = 50$.
The time formula assumes uniform (constant) speed. When speed varies, average speed must be used: $S_{\text{avg}} = \frac{\text{Total distance}}{\text{Total time}}$.
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