How to Solve: Speed, Distance, Time

How to Solve: Speed, Distance, Time

(For Students Who Want to Ace Their Exam & Teachers Who Need a Ready-to-Record Script)

Introduction

"Imagine you’re running late for a train—do you know how fast you need to run to catch it? Or how long a road trip will take if you drive at 60 mph? Speed, distance, and time problems show up in real life AND on your exam—master them, and you’ll solve them in seconds!

What You Need To Know First

Before diving in, make sure you understand: 1. Basic multiplication and division – You’ll need to rearrange formulas. 2. Units of measurement – Kilometers (km), meters (m), hours (h), minutes (min), seconds (s). 3. Simple word problems – How to extract numbers and keywords from a question.

Key Vocabulary

Formulas To Know

(MEMORISE THESE – they’re the foundation of every problem!)

1. Basic Formula (The Magic Triangle)
2. Formula: Speed = Distance ÷ Time
3. Variables:
   • Speed (S) = How fast (km/h, m/s, mph)
   • Distance (D) = How far (km, m, miles)
   • Time (T) = How long (h, min, s)

4. Rearranged versions (MEMORISE ALL THREE):

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

5. Average Speed (When speed changes)

6. Formula: Average Speed = Total Distance ÷ Total Time

7. Why? Because speed isn’t always constant (e.g., traffic, stops).

8. Unit Conversions (Given on exam sheet, but know how to use them!)

9. 1 hour = 60 minutes = 3600 seconds
10. 1 km = 1000 meters
11. 1 mile ≈ 1.6 km (check exam sheet for exact value)

Step-by-Step Method

(Follow these steps for EVERY problem—no shortcuts!)

1. Read the question carefully. Underline the given values and what you need to find.
2. Write down the formula that matches what you’re solving for (Speed? Distance? Time?).
3. Check units. Convert if needed (e.g., minutes → hours, meters → km).
4. Plug in the numbers into the formula.
5. Calculate and simplify. Show all working—examiners give marks for steps!
6. Add units to your answer. (e.g., km/h, not just a number).
7. Double-check: Does the answer make sense? (e.g., 1000 km/h for a car? Probably wrong!)

Worked Example Using the Steps

Question: A car travels 240 km in 3 hours. What is its speed?

1. Given: Distance (D) = 240 km, Time (T) = 3 h. Find: Speed (S).
2. Formula: Speed = Distance ÷ Time
3. Units: Already in km and h—no conversion needed.
4. Plug in: S = 240 km ÷ 3 h
5. Calculate: S = 80 km/h
6. Answer: 80 km/h
7. Check: 80 km/h is reasonable for a car.

Worked Examples

Example 1 – Basic (Finding Speed)

Question: A cyclist covers 30 km in 2 hours. What is their speed?

Solution: 1. Given: D = 30 km, T = 2 h. Find: S. 2. Formula: S = D ÷ T 3. Units: km and h—no conversion. 4. Plug in: S = 30 km ÷ 2 h 5. Calculate: S = 15 km/h 6. Answer: 15 km/h What we did and why: We used the basic formula because we had distance and time and needed speed.

Example 2 – Medium (Finding Time with Unit Conversion)

Question: A train travels 180 km at a speed of 60 km/h. How long does the journey take in minutes?

Solution: 1. Given: D = 180 km, S = 60 km/h. Find: T (in minutes). 2. Formula: T = D ÷ S 3. Units: km and h—no conversion yet. But answer needs minutes! 4. Plug in: T = 180 km ÷ 60 km/h = 3 h 5. Convert hours to minutes: 3 h × 60 min/h = 180 min 6. Answer: 180 minutes What we did and why: We found time in hours first, then converted to minutes because the question asked for it.

Example 3 – Exam Style (Average Speed with Stops)

Question: Sarah drives 120 km to a city at 60 km/h. She stops for 30 minutes, then drives back at 40 km/h. What is her average speed for the whole trip?

Solution: 1. Given:
- Outbound: D = 120 km, S = 60 km/h
- Stop: 30 min (0.5 h)
- Return: D = 120 km, S = 40 km/h
- Find: Average speed for whole trip. 2. Formula: Average Speed = Total Distance ÷ Total Time 3. Calculate Total Distance:
- Outbound + Return = 120 km + 120 km = 240 km 4. Calculate Total Time:
- Outbound time: T = D ÷ S = 120 km ÷ 60 km/h = 2 h
- Stop time: 0.5 h
- Return time: T = 120 km ÷ 40 km/h = 3 h
- Total time: 2 h + 0.5 h + 3 h = 5.5 h 5. Plug into average speed formula:
- Avg. Speed = 240 km ÷ 5.5 h ≈ 43.64 km/h 6. Answer: 43.6 km/h (rounded to 1 decimal place) What we did and why: We calculated total distance and total time separately, then used the average speed formula. The stop time must be included in total time!

Common Mistakes

Exam Traps

1-Minute Recap

(Speak naturally, as if talking to a friend the night before the exam.)

"Okay, let’s lock this in. Speed, distance, time—it’s all about one formula: Speed = Distance ÷ Time. But you’ve got to know how to flip it: Distance = Speed × Time, and Time = Distance ÷ Speed. Draw the magic triangle if it helps!

For average speed: Total distance divided by total time—never just average the speeds. And watch out for unit traps—if speed is in km/h, time must be in hours, not minutes.

Exam day tip: Underline the numbers, write the formula, plug in, and always check your units. If your answer is 1000 km/h for a bike, you’ve messed up!

You’ve got this—go ace that exam!