Speed, Distance & Time

Video coming soon3 worked examples

Theory

The Golden Rule: The most common mistake candidates make in this entire course is misinterpreting decimal time. You must remember that there are 60 minutes in an hour, not 100. Therefore, a time of 4.3 hours is not 4 hours and 3 minutes.

1. The Formula Triangle

You must know how to calculate Speed, Distance, and Time. All three come from one relationship:

D = S \times T

which rearranges to give the other two:

S = \frac{D}{T} \qquad\qquad T = \frac{D}{S}

In words:

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

2. Decimal Time Conversions

You cannot multiply or divide using a time like "2 hours 15 minutes" on a calculator. You must convert it into a decimal first.

Minutes to Decimal: Divide the minutes by 60. (Example: 15 mins ÷ 60 = 0.25, so 2 hours 15 mins is 2.25 hours).
Decimal to Minutes: Multiply the decimal part by 60. (Example: for 4.3 hours, calculate 0.3 × 60 = 18 mins, so the time is 4 hours 18 mins).

3. Multi-stage Journeys & Timetables

Exam questions frequently involve journeys with stops or breaks. You must add the driving time to the break time to find the total journey time before working backwards or forwards to find departure or arrival times.

4. Unit Consistency

Make sure your units match perfectly. If a question asks for a speed in kilometres per hour (km/h) but gives you the distance in miles, you must use a conversion factor (e.g., 1 mile = 1.609 km) to convert the distance before calculating the speed.

⚠️ Common Examiner Traps

The "Decimal Time" Trap: Candidates frequently lose marks by writing 3 ½ hours as 3.30 hours in their calculator. It must be written as 3.5 hours.
The "Hidden Stop" Trap: A question will describe a journey and provide the speed and distance, but embed a phrase like "she stopped for 50 minutes for breakfast" in the text. Candidates eagerly calculate the drive time but forget to include the break when calculating the final arrival/departure time.
The "Wrong Units" Trap: a question will often give the time in minutes (e.g., 45 minutes) but ask for the speed in miles per hour. Candidates divide the distance by 45 rather than converting the time to 0.75 hours first.

Worked examples

Example 1

David travels to a conference 148 miles away at an average speed of 40 mph. He arrives at 11:10 am. During his journey, he stopped for 45 minutes for breakfast. Determine the time David left home. (3 marks)

Step 1: Calculate the driving time using $T = D \div S$ .

148 \div 40 = 3.7 \text{ hours}

Step 2: Convert the decimal time into hours and minutes.

0.7 \times 60 = 42 \text{ minutes}

The drive time is 3 hours 42 minutes.

Step 3: Add the break to find the total journey time.

3 hours 42 minutes + 45 minutes = 4 hours 27 minutes.

Step 4: Subtract the total journey time from the arrival time (11:10 am).

11:10 am - 4 hours = 07:10 am.

07:10 am - 27 minutes = 06:43 am.

Final Answer: David left home at 06:43 am.

Example 2

Sarah cycles 8.5 miles in exactly 48 minutes. Calculate Sarah's average speed. Give your answer in kilometres per hour. (1 mile = 1.609 km) (3 marks)

Step 1: Convert the distance from miles into kilometres.

8.5 \times 1.609 = 13.6765 \text{ km}

Step 2: Convert the time from minutes into hours (divide by 60).

48 \div 60 = 0.8 \text{ hours}

Step 3: Calculate the speed using $S = D \div T$ .

13.6765 \div 0.8 = 17.095625

Final Answer: Sarah's average speed is 17.10 km/h (rounded to 2 d.p.).

Example 3

A train travels at an average speed of 84 mph for 2 hours and 24 minutes. Calculate the distance travelled by the train. (2 marks)

Step 1: Convert the time into a decimal.

24 \div 60 = 0.4

The total time is 2.4 hours.

Step 2: Calculate the distance using $D = S \times T$ .

84 \times 2.4 = 201.6

Final Answer: The train travelled 201.6 miles.

Ready to practise?

11 Speed Distance and Time questions with answers and video solutions