Time, Speed & Distance

When Distance is same.

• Rule: $S_1 : S_2 = a : b \implies T_1 : T_2 = b : a$.
• Use for 'Late/Early' problems to find exact time difference units.

Not $(S_1+S_2)/2$.

• Case A (Equal Distances): Harmonic Mean 2xyx+y.
• Case B (Equal Time): Arithmetic Mean x+y2.
• General: Total Distance / Total Time.

Moving bodies.

• Opposite Direction: Add Speeds ($S_1 + S_2$).
• Same Direction: Subtract Speeds ($S_1 - S_2$).
• Used for Meeting Times and Overtaking.

Distance is never zero.

• Crossing Pole: Dist = Train Length ($L_T$).
• Crossing Platform/Train: Dist = $L_T + L_P$.
• Speed is Relative Speed if object moves.

River flow adds or subtracts.

• Downstream (Along): $B + S$.
• Upstream (Against): $B - S$.
• Formulas: $B = (D+U)/2$, $S = (D-U)/2$.

Giving a 'start'.

• Start of distance: A beats B by $x$ meters.
• Start of time: A beats B by $t$ seconds.
• Dead Heat: Both reach at same time.

Meeting on track.

• First Meeting: $L / S_{rel}$.
• Meeting at Start: LCM($T_1, T_2$).
• Distinct Points: $S_1/S_2$ reduced ratio $(a/b)$. Points = $a+b$ (Opp) or $|a-b|$ (Same).