Episode 8 — Aptitude and Reasoning / 8.11 — Speed Distance and Time
8.11 Quick Revision -- Speed, Distance, and Time
Core Formula Triangle
+-------+
| D |
+---+---+
/ | \
/ ---------\
/ | | \
+---+--+ +--+---+
| S | | T |
+------+ +------+
D = S x T S = D / T T = D / S
Unit Conversion
+---------------------------------------------+
| km/h ---> m/s : Multiply by 5/18 |
| m/s ---> km/h: Multiply by 18/5 |
+---------------------------------------------+
Quick Reference:
18 km/h = 5 m/s 36 = 10 54 = 15
72 = 20 90 = 25 108 = 30
Proportionality (Same Distance)
S1 x T1 = S2 x T2 (because D is constant)
Speed UP by 1/n --> Time DOWN by 1/(n+1)
Speed DOWN by 1/n --> Time UP by 1/(n-1)
Relative Speed
Same Direction: |S1 - S2|
Opposite Direction: S1 + S2
Average Speed
General: Total Distance / Total Time
Equal Distance: 2 x S1 x S2 / (S1 + S2) [Harmonic mean]
Equal Time: (S1 + S2) / 2 [Arithmetic mean]
Three speeds (equal dist): 3.S1.S2.S3 / (S1.S2 + S2.S3 + S1.S3)
Meeting Problems
A ------> <------ B (D apart)
Time to meet = D / (Sa + Sb)
Meeting point from A = Sa x D / (Sa + Sb)
Ratio of distances = Sa : Sb
Overtaking Problems
A ------> gap G B ------> (Sa > Sb)
Time to overtake = G / (Sa - Sb)
Late / Early Formula
At S1 --> t1 late; At S2 --> t2 early
Distance = S1 x S2 x (t1 + t2) / (S2 - S1)
Both late: use (t1 - t2) instead of (t1 + t2)
Stoppage
Minutes stopped per hour = [(S - S') / S] x 60
Circular Track
Same direction: Time to meet = L / |S1 - S2|
Opposite direction: Time to meet = L / (S1 + S2)
Meet at start: LCM(L/S1, L/S2)
Speed-Time-Distance Ratios
If speeds in ratio a : b
--> Times (same distance) in ratio b : a
--> Distances (same time) in ratio a : b
Key Traps to Avoid
1. Average speed ≠ average of speeds (use harmonic mean for equal dist)
2. Convert units BEFORE plugging into formulas
3. Minutes to hours: divide by 60 (NOT by 100)
4. "Late by 20 min" and "early by 10 min" --> gap = 30 min
5. Speed increase of 25% does NOT mean time decrease of 25%
(it decreases by 20%)
Quick Percentage Table
Speed Change | Time Change (same distance)
--------------|-----------------------------
+25% | -20%
+50% | -33.3%
+100% | -50%
-20% | +25%
-25% | +33.3%
-50% | +100%
Problem-Solving Checklist
[ ] Identify what is given: S, D, or T (and which to find)
[ ] Check if units match (all km/h or all m/s)
[ ] Determine if same direction or opposite direction
[ ] For average speed: check if equal distance or equal time
[ ] For meeting: use sum of speeds
[ ] For overtaking: use difference of speeds
[ ] Verify answer makes sense (speed > 0, time > 0)
Part of Section 8.11: Speed, Distance, and Time