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Basic Formula & Direct Conversion

Introduction

Every Time, Speed, and Distance problem starts with a simple but powerful relationship. Understanding this foundation helps you solve any question about motion, travel, or speed - whether it’s a car journey, a train, or a person walking.

This pattern builds your base to calculate distance, speed, or time when any two of them are known.

Pattern: Basic Formula & Direct Conversion

Pattern

The key formula is: Speed = Distance ÷ Time

From this, you can easily rearrange to find any missing quantity:

  • Distance = Speed × Time
  • Time = Distance ÷ Speed

Remember: Units must be consistent - if distance is in km, time should be in hours (speed in km/h); if distance is in meters, time should be in seconds (speed in m/s).

Step-by-Step Example

Question

A car travels 150 km in 3 hours. Find its speed.

Solution

  1. Step 1: Identify Given Values

    Distance = 150 km, Time = 3 hours.

  2. Step 2: Apply the Formula

    Use Speed = Distance ÷ Time.

  3. Step 3: Substitute and Calculate

    Speed = 150 ÷ 3 = 50 km/h.

  4. Final Answer:

    Speed of the car = 50 km/h.

  5. Quick Check:

    If the car moves at 50 km/h for 3 hours → Distance = 50 × 3 = 150 km ✅ (Correct!)

Quick Variations

1. Given speed and time → Find distance.

2. Given distance and speed → Find time.

3. Direct unit conversion problems (e.g., convert km/h to m/s).

4. Comparative travel problems using same formula in different cases.

Trick to Always Use

  • Step 1: Write the base formula (S = D ÷ T).
  • Step 2: Check and align all units before substituting values.
  • Step 3: Use the “Triangle Formula” visual (D on top, S and T at bottom) to remember rearrangements.
  • Step 4: Verify by substituting back into D = S × T.

Summary

Summary

  • Formula to remember: S = D ÷ T.
  • Rearrange easily: D = S × T and T = D ÷ S.
  • Keep units consistent (km-km/h-hr or m-m/s-s).
  • Always cross-check your final answer using the opposite formula.

Practice

(1/5)
1. A cyclist covers 60 km in 4 hours. Find his speed.
easy
A. 15 km/h
B. 12 km/h
C. 20 km/h
D. 18 km/h

Solution

  1. Step 1: Identify Given Values

    Distance = 60 km, Time = 4 hours.

  2. Step 2: Apply Formula

    Speed = Distance ÷ Time.

  3. Step 3: Substitute and Calculate

    Speed = 60 ÷ 4 = 15 km/h.

  4. Final Answer:

    Speed = 15 km/h → Option A.

  5. Quick Check:

    15 × 4 = 60 ✅
Hint: Speed = Distance ÷ Time - divide distance by time directly.
Common Mistakes: Forgetting to divide correctly or mixing up units.
2. A car runs at a speed of 60 km/h for 2 hours. How much distance does it cover?
easy
A. 100 km
B. 110 km
C. 120 km
D. 150 km

Solution

  1. Step 1: Identify Given Values

    Speed = 60 km/h, Time = 2 hours.

  2. Step 2: Apply Formula

    Distance = Speed × Time.

  3. Step 3: Substitute and Calculate

    Distance = 60 × 2 = 120 km.

  4. Final Answer:

    Distance = 120 km → Option C.

  5. Quick Check:

    120 ÷ 2 = 60 km/h ✅
Hint: Multiply speed and time directly to find distance.
Common Mistakes: Dividing instead of multiplying.
3. A train covers 240 km at a uniform speed of 80 km/h. Find the time taken.
easy
A. 2 hours
B. 3 hours
C. 4 hours
D. 5 hours

Solution

  1. Step 1: Identify Given Values

    Distance = 240 km, Speed = 80 km/h.

  2. Step 2: Apply Formula

    Time = Distance ÷ Speed.

  3. Step 3: Substitute and Calculate

    Time = 240 ÷ 80 = 3 hours.

  4. Final Answer:

    Time taken = 3 hours → Option B.

  5. Quick Check:

    80 × 3 = 240 ✅
Hint: Use Time = Distance ÷ Speed when speed is given.
Common Mistakes: Reversing formula as Speed ÷ Distance.
4. A person walks at 5 km/h for 2 hours and then runs at 10 km/h for 1 hour. Find total distance covered.
medium
A. 15 km
B. 25 km
C. 30 km
D. 20 km

Solution

  1. Step 1: Split Movements

    First part: 5 km/h × 2 h = 10 km. Second part: 10 km/h × 1 h = 10 km.

  2. Step 2: Add Distances

    Total Distance = 10 + 10 = 20 km.

  3. Final Answer:

    Total distance = 20 km → Option D.

  4. Quick Check:

    Average speed = 20 ÷ 3 ≈ 6.67 km/h (logical) ✅
Hint: Break the journey into parts and sum distances.
Common Mistakes: Adding speeds instead of distances.
5. A bus travels 90 km at 45 km/h and returns the same distance at 30 km/h. Find the total time taken for the trip.
medium
A. 5 hours
B. 3 hours
C. 4 hours
D. 6 hours

Solution

  1. Step 1: Identify Given Values

    Onward: 90 km at 45 km/h; Return: 90 km at 30 km/h.

  2. Step 2: Find Time for Each Part

    Onward time = 90 ÷ 45 = 2 h; Return time = 90 ÷ 30 = 3 h.

  3. Step 3: Add Total Time

    Total time = 2 + 3 = 5 hours.

  4. Final Answer:

    Total time = 5 hours → Option A.

  5. Quick Check:

    Total distance = 180 km, average speed = (2×45 + 3×30) / 5 = 36 km/h ⇒ 180 ÷ 36 = 5 h ✅
Hint: Calculate each leg separately using Time = Distance ÷ Speed.
Common Mistakes: Averaging speeds instead of using time formula.

Mock Test

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