Master Time, Speed & Distance from Zero

Speed, Time, and Distance are related by a simple triangle formula. If you travel 100 km in 2 hours, your speed is 50 km/hr. The three formulas: Speed = Distance/Time, Distance = Speed×Time, Time = Distance/Speed. Always check units — km/hr or m/s!

Key Formulas

Basic Relation

Speed = Distance / Time

The triangle formula — cover D to get S×T, cover S to get D/T, cover T to get D/S.

Unit Conversion

km/hr × 5/18 = m/s

To convert km/hr to m/s, multiply by 5/18. Reverse: multiply by 18/5.

Average Speed

Avg Speed = 2xy/(x+y) for equal distances

When same distance covered at speed x and y.

Relative Speed

Same direction: (u-v). Opposite direction: (u+v)

Very important for train problems!

⚡ Shortcut Tricks

km/h to m/s: multiply by 5/18. m/s to km/h: multiply by 18/5. Memorize this!

Relative speed SAME direction: S1 - S2. Relative speed OPPOSITE direction: S1 + S2.

Average speed — DIFFERENT distances and times: Total distance / Total time.

Average speed — SAME distance at two speeds: 2×S1×S2 / (S1+S2). NEVER just average the speeds!

Average speed — SAME time: Simple average of all speeds works ONLY when time is equal in each part.

Circular race: Time to meet at starting point = LCM of individual round times.

Late/early problem: Distance = S1×S2×(T1+T2) / (S1-S2) where T1=late time, T2=early time.

Chase problem: Time to catch = Initial gap / Relative speed.

✏️ Solved Examples

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