Time And Distance Concept and Class Notes and PDFs Practice sets By Wisdom Helps

Time & Distance — Complete Notes, Definitions, Formulas & Shortcuts

Author: Wisdom Helps | Topic: Time and Distance (Full depth)

1. Basic Definitions

• Distance (D): The length of the path traveled (units: m, km, miles).
• Speed (S): Rate of covering distance (units: m/s, km/h, mph).
• Time (T): Duration taken (units: s, min, hr).

2. Fundamental Formula

      D  = S  × T 

So the three forms are:

• [S = D / T] (Speed = Distance ÷ Time)
• [D = S × T] (Distance = Speed × Time)
• [T = D / S] (Time = Distance ÷ Speed)

Shortcut: Cover the variable you want in the triangle — the remaining two give the formula.

3. Unit Conversions

• [1 km/h = 5/18 m/s]
• [1 m/s = 18/5 km/h]
• Time: 1 min = 60 sec; 1 hr = 60 min = 3600 sec

4. Average Speed

When equal distance is covered at two speeds x and y:

[Average speed = (2xy) / (x + y)] (for equal distances)

For different distances d₁, d₂ with speeds s₁, s₂:

[Average speed = (d1 + d2) / (d1/s1 + d2/s2)]

Note: Don't use simple average of speeds unless times (not distances) are equal.

5. Relative Speed

• Same direction: [Relative speed = |S₁ − S₂|]
• Opposite direction: [Relative speed = S₁ + S₂]

6. Important Problem Types & Formulas

Train problems (crossing)

• Train length L crosses a stationary object in time T: [Speed = L / T].
• Two trains of lengths L₁ and L₂ crossing each other: [Time = (L₁ + L₂) / RelativeSpeed].

Boats: Upstream & Downstream

• [Downstream = Boat + Stream]
• [Upstream = Boat − Stream]
• [Boat = (Down + Up) / 2] and [Stream = (Down − Up) / 2]

Meeting on a circular track

Meeting time = [Total distance / Relative speed]. (Pick relative speed by direction.)

7. Useful Shortcuts & Tricks

• If speeds ratio is a:b, times ratio = b:a. [inverse]
• If speed ↑ by x%, time ↓ by [x / (100 + x) × 100%]. If speed ↓ by x%, time ↑ by [x / (100 − x) × 100%].
• For many exam shortcuts, cancel constants early — only ratios may matter.

8. Worked Examples (step-by-step)

Example 1: A car goes 150 km at 50 km/h. How long?
Step 1: Use [T = D / S].
Step 2: T = 150 / 50 = 3 hours.

Answer: [3 hours]

Example 2: Trains 120 m and 80 m approach each other with speeds 36 km/h and 54 km/h. Time to cross?
Step 1: Convert speeds to m/s: 36 → 36×(5/18)=10 m/s; 54 → 54×(5/18)=15 m/s.
Step 2: Relative speed = 10 + 15 = 25 m/s.
Step 3: Total length = 120 + 80 = 200 m.
Step 4: Time = 200 / 25 = 8 seconds.

Answer: [8 seconds]

Example 3 (Average speed): 60 km at 30 km/h and 60 km at 60 km/h. Average speed?
Step 1: Equal distances → use [(2xy) / (x + y)].
Step 2: Avg = 2×30×60 / (30 + 60) = 3600 / 90 = 40 km/h.

Answer: [40 km/h]

Quick Reference

• [S = D / T]
• [D = S × T]
• [T = D / S]
• [1 km/hr = 5/18 m/s]
• [Average for equal distances = (2xy) / (x + y)]

Watch the following video class for a complete understanding — starting from the basics and moving up to advanced-level questions.
All the problems discussed are previous year questions, solved in detail during the class.

✅ Free PDFs are provided for download
✅ Practice sets are included for extra preparation

📘 Time and Distance – Class 1

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