Distance, Speed, and Time: Civil Service Exam Guide
Distance, speed, and time problems are among the most frequently tested items in the Civil Service Exam (CSE), especially in the Numerical Ability section. These questions may appear simple at first glance, yet many test-takers struggle because they do not fully understand the underlying relationships between these three concepts. This guide provides a complete, beginner-friendly explanation and practical strategies to help you confidently solve any distance–speed–time problem on the exam.
Understanding the Core Formula
All distance, speed, and time problems come down to one simple formula:
Distance = Speed × Time
From this, we can derive two additional formulas:
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Speed = Distance ÷ Time
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Time = Distance ÷ Speed
These three equations are the foundation. If you memorize them and understand when to apply each one, most questions become straightforward.
Visualizing the Relationship
You can think of distance–speed–time as a triangle:
Cover the value you want to solve for:
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Cover Distance, and you’re left with Speed × Time
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Cover Speed, and you’re left with Distance ÷ Time
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Cover Time, and you’re left with Distance ÷ Speed
This mental shortcut helps you avoid confusion during the exam.
Key Units and Conversions You Must Know
Many questions require converting units before solving. The most common conversions are:
1. Converting Hours to Minutes
1 hour = 60 minutes
Example: 2 hours 30 minutes = 2.5 hours = 150 minutes
2. Converting Minutes to Hours
Divide by 60.
Example: 45 minutes = 45 ÷ 60 = 0.75 hours.
3. Converting km/h to m/s
Multiply by 5/18
Example: 54 km/h × 5/18 = 15 m/s
4. Converting m/s to km/h
Multiply by 18/5
Example: 20 m/s × 18/5 = 72 km/h
Common Question Types in the CSE
The exam uses a variety of patterns, and understanding them helps you solve faster. Below are the most common types.
Type 1: Basic Distance, Speed, and Time Questions
These simply ask you to compute one value given the other two.
Example:
A car travels at 60 km/h for 2 hours. How far does it travel?
Solution: Distance = 60 × 2 = 120 km
Type 2: Finding Speed or Time
These are often disguised in word problems.
Example:
A person walks 5 km in 1 hour. What is their speed?
Speed = 5 ÷ 1 = 5 km/h
Type 3: Two Moving Objects in Opposite Directions
When two objects move away from or toward each other:
Example (Opposite):
Two cars start at the same point and travel in opposite directions at 40 km/h and 50 km/h.
Their rate of separation = 40 + 50 = 90 km/h
Type 4: Two Moving Objects in the Same Direction
Often used for catching-up or overtaking problems.
Example:
Car A travels at 80 km/h. Car B follows at 100 km/h.
Relative speed = 100 – 80 = 20 km/h
Type 5: Average Speed Problems
Average speed is NOT simply the average of speeds. Use this formula:
Average Speed = Total Distance ÷ Total Time
Example:
A person walks 10 km at 5 km/h and another 10 km at 10 km/h.
Time1 = 10 ÷ 5 = 2 hours
Time2 = 10 ÷ 10 = 1 hour
Average Speed = 20 ÷ 3 = 6.67 km/h
Type 6: Round-Trip Problems
When the speed going and returning differs, always compute time separately.
Type 7: Trains and Relative Speed Problems
Trains often involve:
Formula:
Time to pass = Total Distance ÷ Relative Speed
Type 8: Boats and Streams
Key terms:
Strategies for Solving CSE Distance Problems Quickly
1. Identify what the question is really asking
Is it asking for speed? time? or distance?
2. Convert all units before solving
Don’t mix km/h with minutes or meters.
3. Use relative speed for problems with two moving objects
4. Draw simple diagrams
This reduces confusion.
5. Avoid mental math if the numbers are tricky
Write them down.
Sample Problems with Solutions
Below are exam-style examples to strengthen your understanding.
Problem 1: Basic Computation
A man travels 90 km in 3 hours. What is his speed?
Solution:
Speed = Distance ÷ Time = 90 ÷ 3 = 30 km/h
Problem 2: Finding Time
A bus travels at 50 km/h. How long will it take to travel 125 km?
Time = Distance ÷ Speed = 125 ÷ 50 = 2.5 hours
Problem 3: Opposite Direction
Two people start walking from the same point. One walks east at 4 km/h, the other west at 5 km/h. How fast are they separating?
Relative speed = 4 + 5 = 9 km/h
Problem 4: Same Direction (Overtaking)
A truck moves at 70 km/h and a car follows at 90 km/h. What is their relative speed?
Relative speed = 90 – 70 = 20 km/h
Problem 5: Train and Platform
A 200-meter train travels at 54 km/h. How long does it take to pass a person?
Convert speed:
54 × 5/18 = 15 m/s
Time = Distance ÷ Speed = 200 ÷ 15 = 13.33 seconds
Problem 6: Round Trip
A man walks to work at 4 km/h and returns at 6 km/h. If each way is 3 km, what is his average speed?
Time1 = 3 ÷ 4 = 0.75
Time2 = 3 ÷ 6 = 0.5
Total distance = 6 km
Total time = 1.25 hours
Average speed = 6 ÷ 1.25 = 4.8 km/h
Problem 7: Boat in Stream
A boat moves at 12 km/h in still water. Stream speed is 3 km/h. What is the upstream speed?
Upstream = 12 – 3 = 9 km/h
Higher-Level Practice Problems
Below are more challenging problems similar to those seen in actual Civil Service Exams.
Problem 8
A cyclist travels 8 km in 20 minutes. What is his speed in km/h?
Convert time: 20 minutes = 20/60 = 1/3 hour
Speed = 8 ÷ (1/3) = 8 × 3 = 24 km/h
Problem 9
A car increases its speed from 60 km/h to 80 km/h. How much time is saved on a 120 km trip?
Time at 60 km/h = 120 ÷ 60 = 2 hours
Time at 80 km/h = 120 ÷ 80 = 1.5 hours
Time saved = 0.5 hours = 30 minutes
Problem 10
Two trains 150 m each travel in opposite directions at 60 km/h and 40 km/h. How long will they take to pass each other?
Convert speed:
Total speed = 60 + 40 = 100 km/h = 100 × 5/18 = 27.78 m/s
Total distance = 150 + 150 = 300 m
Time = 300 ÷ 27.78 ≈ 10.8 seconds
Tips for Avoiding Common Mistakes
1. Forgetting to convert minutes to hours
Many errors occur because test-takers solve using mismatched units.
2. Averaging speeds incorrectly
Always compute total time and total distance.
3. Wrong relative speed
Add speeds if moving towards or away, subtract if in the same direction.
4. Misunderstanding train questions
Remember: length of train matters.
5. Not simplifying fractions
CSE often uses numbers that simplify easily—take advantage of that.
How to Practice Effectively
To master these problems:
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Solve 20–30 questions daily
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Mix easy and difficult questions
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Practice under time pressure
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Review mistakes immediately
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Memorize the core formulas until automatic
Distance–speed–time problems reward consistency and familiarity, which come through repeated exposure.
Final Advice for the Civil Service Exam
Distance, speed, and time questions typically appear 3–7 times in the Numerical Ability section. With solid understanding and steady practice, you can easily master this topic. Focus on:
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Knowing the formulas
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Identifying question type
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Converting units correctly
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Practicing relative speed
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Solving systematically
By applying the strategies in this guide, you’ll be able to solve these problems accurately and quickly on exam day.
Problems Sets
Problem 1
A car travels at 60 km/h for 2.5 hours. How far does it go?
Problem 2
A runner covers 12 kilometers in 1 hour and 30 minutes. What is the runner’s speed in km/h?
Problem 3
How long will it take to travel 180 km at a speed of 90 km/h?
Problem 4
A cyclist travels at 15 km/h. How far will the cyclist travel in 40 minutes?
Problem 5
Two cars travel in opposite directions at speeds of 50 km/h and 70 km/h. How far apart are they after 3 hours?
Problem 6
A man walks at 5 km/h. How long will it take him to walk 8 km?
Problem 7
A bus travels 150 km at 75 km/h. How much time does it take?
Problem 8
A plane flies 600 km in 1.5 hours. What is its speed?
Problem 9
A truck increases its speed from 60 km/h to 80 km/h. How much time is saved on a 160 km trip?
Problem 10
A 300-meter train travels at 72 km/h. How long will it take to pass a person?
Problem 11
A boat travels at 12 km/h in still water. The stream flows at 3 km/h. What is the downstream speed?
Problem 12
The same boat travels upstream. What is the upstream speed?
Problem 13
A student walks to school at 4 km/h and returns at 6 km/h. Each way is 2 km. What is the average speed?
Problem 14
Two trains, each 120 meters long, travel in opposite directions at 54 km/h and 36 km/h. How long will they take to pass each other?
Problem 15
A vehicle travels 90 km at 30 km/h and another 90 km at 60 km/h. What is the average speed for the whole trip?
Problem 16
A boy runs at 6 m/s. How far can he run in 25 seconds?
Problem 17
A car travels 120 km in 1 hour and 20 minutes. What is its speed?
Problem 18
A 400-meter train passes a 200-meter platform in 25 seconds. What is the speed of the train in km/h?
Problem 19
Two cyclists start 45 km apart and move toward each other. One rides at 12 km/h and the other at 18 km/h. How long before they meet?
Problem 20
A car travels at 50 km/h for 3 hours and at 80 km/h for 2 hours. What distance did it cover?
Answer Keys
Answer 1
Distance = 60 × 2.5 = 150 km
Answer 2
1.5 hours
Speed = 12 ÷ 1.5 = 8 km/h
Answer 3
Time = 180 ÷ 90 = 2 hours
Answer 4
40 min = 2/3 hour
Distance = 15 × (2/3) = 10 km
Answer 5
Relative speed = 50 + 70 = 120 km/h
Distance apart = 120 × 3 = 360 km
Answer 6
Time = 8 ÷ 5 = 1.6 hours (1 hour 36 minutes)
Answer 7
Time = 150 ÷ 75 = 2 hours
Answer 8
Speed = 600 ÷ 1.5 = 400 km/h
Answer 9
Time at 60 km/h = 2.67 hours
Time at 80 km/h = 2 hours
Time saved = 0.67 hour = 40 minutes
Answer 10
72 km/h = 20 m/s
Time = 300 ÷ 20 = 15 seconds
Answer 11
Downstream speed = 12 + 3 = 15 km/h
Answer 12
Upstream speed = 12 − 3 = 9 km/h
Answer 13
Time going = 0.5 hr
Time returning = 0.33 hr
Total distance = 4 km
Total time = 0.83 hr
Average speed ≈ 4.82 km/h
Answer 14
Relative speed = 90 km/h = 25 m/s
Total distance = 240 m
Time = 240 ÷ 25 = 9.6 seconds
Answer 15
Time1 = 3 hr
Time2 = 1.5 hr
Total distance = 180 km
Total time = 4.5 hr
Average speed = 40 km/h
Answer 16
Distance = 6 × 25 = 150 meters
Answer 17
1 hour 20 min = 1.33 hours
Speed = 120 ÷ 1.33 ≈ 90 km/h
Answer 18
Total distance = 600 m
Speed = 600 ÷ 25 = 24 m/s
Convert = 24 × 18/5 = 86.4 km/h
Answer 19
Relative speed = 30 km/h
Time = 45 ÷ 30 = 1.5 hours
Answer 20
Distance = 150 + 160 = 310 km
