CODEBHAVYA • QUANTITATIVE APTITUDE

🚗 Time, Speed & Distance

Connect distance, speed and time; convert units; compare moving objects; and solve journey, train, boat and race problems.

🎯 1. Learning Objectives

Use the speed–distance–time relationship.
Convert between km/h and m/s.
Calculate average and relative speed.
Solve meeting and journey problems.
Handle trains, platforms and moving observers.
Solve boats, streams and circular-track questions.

📖 2. Basic Relationship

Speed

Speed = Distance ÷ Time

Distance

Distance = Speed × Time

Time

Time = Distance ÷ Speed

Consistency

Distance and time units must match the unit used for speed before calculating.

🔄 3. Unit Conversions

km/h to m/s

Multiply by 5/18

m/s to km/h

Multiply by 18/5

Speed	Equivalent
18 km/h	5 m/s
36 km/h	10 m/s
54 km/h	15 m/s
72 km/h	20 m/s
90 km/h	25 m/s

📊 4. Average Speed

Average speed is total distance divided by total time. It is not normally the simple average of speeds.

General Journey

Average speed = total distance/total time

Equal Distances at x and y

Average speed = 2xy/(x+y)

Equal Times at x and y

Average speed = (x+y)/2

Round Trip

Use total outward plus return distance divided by total outward plus return time.

↔️ 5. Relative Speed

Same Direction

Relative speed = |x−y|

Opposite Directions

Relative speed = x+y

Meeting Time

Initial separation ÷ relative speed

Overtaking Time

Gap ÷ speed difference

🚆 6. Trains

Crossing a Pole or Person

Time = train length/relative speed

Crossing a Platform

Time = (train length+platform length)/speed

Two Trains

Time = sum of lengths/relative speed

Required Unit

Convert train speed from km/h to m/s when lengths are in metres.

🚤 7. Boats and Streams

Downstream Speed

Boat speed + stream speed

Upstream Speed

Boat speed − stream speed

Still-Water Speed

(Downstream+upstream)/2

Stream Speed

(Downstream−upstream)/2

🏁 8. Races and Circular Tracks

Linear Race

For the same time, distances covered are proportional to speeds.

Opposite Directions on a Track

Meeting time = track length ÷ sum of speeds.

Same Direction on a Track

Catch-up time = track length ÷ difference of speeds.

Number of Rounds

Distance covered divided by track length gives completed rounds.

🗺️ 9. Journey-Based Problems

Late and Early Arrival

Write the travel time at each speed and compare both with the scheduled time.

Stops and Delays

Add stoppage time to moving time before calculating the journey's overall average speed.

INTERACTIVE EXPLORER

🧪 10. Journey Explorer

Choose a problem type, enter the values and click Calculate. Changing a value hides the old result.

Calculation type

Value A

Value B

Value C

Select a calculation or example, then click Calculate.

🧾 11. Solved Examples

Example 1: Basic Speed

Problem: Travel 120 km in 2 hours.

Solution: Speed=120/2=60 km/h.

Example 2: Equal Distances

Problem: Equal distances at 40 and 60 km/h.

Solution: Average=2×40×60/(40+60)=48 km/h.

Example 3: Train

Problem: A 120 m train at 54 km/h crosses a pole.

Solution: 54 km/h=15 m/s; time=120/15=8 seconds.

Example 4: Boat

Problem: Boat speed 12 km/h, stream speed 3 km/h.

Solution: Downstream=15 km/h; upstream=9 km/h.

💻 12. Applications in Programming

Navigation Systems

Estimate arrival time from route distance, traffic-adjusted speed and delays.

Delivery Tracking

Calculate travelled distance, remaining time and average delivery speed.

Simulation

Update object position using velocity and elapsed time.

Collision Detection

Use relative position and relative speed to predict meeting times.

⚠️ 13. Common Mistakes

Mixing Units

Convert hours, minutes, kilometres and metres before applying formulas.

Averaging Speeds Directly

Use total distance/total time unless equal-time travel is explicitly given.

Wrong Relative Operation

Add speeds for opposite directions and subtract for the same direction.

Ignoring Train Length

A train must cover its own length when crossing a pole or person.

✍️ 14. Practice Problems

Solve each problem first, then use Show Solution.

1. Find the speed for 180 km covered in 3 hours.

2. Convert 90 km/h to m/s.

3. Find the average speed for equal distances at 30 and 60 km/h.

4. A 180 m train runs at 72 km/h. Find its pole-crossing time.

5. Boat speed is 15 km/h and stream speed is 4 km/h. Find upstream speed.

📝 15. Quick Revision

Speed=distance/time; distance=speed×time.
km/h→m/s: ×5/18; m/s→km/h: ×18/5.
Average speed=total distance/total time.
Same direction: subtract speeds; opposite directions: add.
Train crossing distance includes the required lengths.
Downstream adds stream speed; upstream subtracts it.

INTERACTIVE PRACTICE

🚗 Time, Speed & Distance Practice

Complete 20 questions. Score, every option, correct answers and explanations appear only after final submission.

Start 20-Question Test →