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Time and Distance
Rumman Ansari
July 28, 2024
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Time and Distance Formulas
Basic Formulas
Speed
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]Distance
\[ \text{Distance} = \text{Speed} \times \text{Time} \]Time
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]Conversions
Speed in km/hr to m/s
\[ \text{Speed (m/s)} = \text{Speed (km/hr)} \times \frac{5}{18} \]Speed in m/s to km/hr
\[ \text{Speed (km/hr)} = \text{Speed (m/s)} \times \frac{18}{5} \]Relative Speed
Same Direction
\[ \text{Relative Speed} = \text{Speed}_1 - \text{Speed}_2 \]Opposite Direction
\[ \text{Relative Speed} = \text{Speed}_1 + \text{Speed}_2 \]Time to Meet
Time to Meet (Same Direction)
\[ \text{Time} = \frac{\text{Distance}}{\text{Relative Speed}} \]Time to Meet (Opposite Direction)
\[ \text{Time} = \frac{\text{Distance}}{\text{Relative Speed}} \]Average Speed
When the same distance is traveled at different speeds:
\[
\text{Average Speed} = \frac{2 \times \text{Speed}_1 \times \text{Speed}_2}{\text{Speed}_1 + \text{Speed}_2}
\]
Examples
Example 1: Finding Speed
\[ \text{If a car travels 150 km in 3 hours, what is its speed?} \] \[ \text{Speed} = \frac{150 \text{ km}}{3 \text{ hours}} = 50 \text{ km/hr} \]Example 2: Finding Time
\[ \text{If a person walks at a speed of 5 km/hr for 10 km, how long does it take?} \] \[ \text{Time} = \frac{10 \text{ km}}{5 \text{ km/hr}} = 2 \text{ hours} \]
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