Understanding Speed, Distance, and Time
Speed, Distance, and Time are fundamental concepts used to describe motion. They are related by a set of simple formulas.
- Distance (D): How far an object travels. Common units include metres (m), kilometres (km), miles.
- Speed (S): How fast an object is travelling. It's the distance travelled per unit of time. Common units include metres per second (m/s), kilometres per hour (km/h), miles per hour (mph).
- Time (T): How long the travel takes. Common units include seconds (s), minutes (min), hours (hr).
It's crucial to use consistent units when performing calculations. For example, if speed is in miles per hour, time should be in hours and distance in miles.
Common Unit Conversions
Being able to convert between units is essential for solving speed, distance, and time problems.
Distance Conversions
1 kilometre (km) = 1000 metres (m)1 mile ≈ 1.6 kilometres (km)(This is a common approximation)1 kilometre (km) ≈ 0.62 miles
Time Conversions
1 hour = 60 minutes1 minute = 60 seconds1 hour = 3600 seconds(60 × 60)- To convert minutes to hours: Divide by 60 (e.g., 30 minutes = 30/60 = 0.5 hours)
- To convert hours to minutes: Multiply by 60 (e.g., 2 hours = 2 × 60 = 120 minutes)
The DST Formula Triangle
A helpful way to remember the formulas is the DST triangle:
To use the triangle:
- Cover the quantity you want to find.
- The remaining two quantities show you the formula:
- To find Distance (D), cover D: Speed × Time (S × T)
- To find Speed (S), cover S: Distance ÷ Time (D / T)
- To find Time (T), cover T: Distance ÷ Speed (D / S)
Distance = Speed × Time
Speed = Distance ÷ Time
Time = Distance ÷ Speed
Worked Examples
1. Calculating Distance
Problem: A car travels at an average speed of 50 mph for 3 hours. How far does it travel?
Given: Speed = 50 mph, Time = 3 hours
Formula: Distance = Speed × Time
Calculation: Distance = 50 mph × 3 hours = 150 miles
Answer: The car travels 150 miles.
2. Calculating Speed
Problem: A cyclist covers a distance of 45 km in 2.5 hours. What is their average speed?
Given: Distance = 45 km, Time = 2.5 hours
Formula: Speed = Distance ÷ Time
Calculation: Speed = 45 km ÷ 2.5 hours = 18 km/h
Answer: The cyclist's average speed is 18 km/h.
3. Calculating Time
Problem: How long will it take to travel 200 miles at an average speed of 40 mph?
Given: Distance = 200 miles, Speed = 40 mph
Formula: Time = Distance ÷ Speed
Calculation: Time = 200 miles ÷ 40 mph = 5 hours
Answer: It will take 5 hours.
4. Unit Conversion (Time)
Problem: A train travels at 80 km/h. How far does it travel in 45 minutes?
Given: Speed = 80 km/h, Time = 45 minutes
Important: Units must be consistent. Speed is in km/h, so time must be in hours.
Workings for Time Conversion:
- There are 60 minutes in 1 hour.
- Convert 45 minutes to hours:
45 minutes / 60 minutes/hour = 0.75 hours(or 3/4 hour).
Formula: Distance = Speed × Time
Calculation: Distance = 80 km/h × 0.75 hours = 60 km
Answer: The train travels 60 km.
Exam-Style Speed, Distance, Time Problems
1. Journey Planning
John needs to drive 180 miles. He estimates his average speed will be 45 mph. If he leaves at 9:30 am, what time will he arrive?
Answer: 1:30 pm
Explanation:
- Calculate the time taken for the journey:
Time = Distance ÷ Speed =180 miles ÷ 45 mph = 4 hours. - Add the journey time to the departure time:
Departure: 9:30 am.
Add 4 hours: 9:30 am + 4 hours = 13:30. - Convert 13:30 to 12-hour clock format: 1:30 pm.
2. Comparing Speeds
Car A travels 210 km in 3 hours. Car B travels 160 km in 2 hours and 30 minutes. Which car is travelling faster, and by how much in km/h?
Answer: Car A is faster by 6 km/h.
Explanation:
- Car A Speed:
Speed = Distance ÷ Time =210 km ÷ 3 hours = 70 km/h. - Car B Time Conversion:
2 hours and 30 minutes =2 + (30/60) hours = 2 + 0.5 hours = 2.5 hours. - Car B Speed:
Speed = Distance ÷ Time =160 km ÷ 2.5 hours = 64 km/h. - Comparison:
Car A (70 km/h) is faster than Car B (64 km/h). - Difference in speed:
70 km/h - 64 km/h = 6 km/h.
Interactive DST Calculator
Enter any two values to calculate the third. Important: Ensure your units are consistent for the two values you enter. For example, if you enter distance in 'km' and time in 'hours', the calculated speed will be in 'km/h'.
Calculated Value: ?
Key Points for Speed, Distance & Time
- Remember the DST triangle to easily recall the formulas.
- Distance = Speed × Time
- Speed = Distance ÷ Time
- Time = Distance ÷ Speed
- Always ensure your units are consistent before calculating (e.g., convert minutes to hours if speed is in miles per hour).
- Read word problems carefully to identify what is given and what needs to be found.