Section B — Chapters 23–39

Distance, Speed, Time and Real-Life Graphs

Junior Cycle — 1st Year

✓By the end of this lesson students will be able to convert between 12-hour and 24-hour clock times.
✓By the end of this lesson students will be able to calculate distance, speed, or time given the other two values.
✓By the end of this lesson students will be able to interpret and construct simple distance-time graphs.
✓By the end of this lesson students will be able to extract and interpret information from various real-life graphs.

Key concepts

Time (12-hour and 24-hour clock)

The 12-hour clock uses AM (ante meridiem, before noon) and PM (post meridiem, after noon). The 24-hour clock uses four digits (HH:MM) and runs from 00:00 (midnight) to 23:59. To convert from 12-hour PM to 24-hour, add 12 to the hour (e.g., 3 PM = 15:00). 12 AM (midnight) is 00:00. 12 PM (noon) is 12:00.

Distance

Distance is the total length covered by an object in motion. It is typically measured in units like kilometres (km) or metres (m).

Speed

Speed is the rate at which an object covers distance. It tells us how fast an object is moving. It is calculated as distance divided by time. Common units include kilometres per hour (km/h) or metres per second (m/s).

Speed = Distance / Time

Time

Time is the duration of an event. It is measured in units like hours (h), minutes (min), or seconds (s).

Relationship between Distance, Speed, Time

These three quantities are linked by specific formulae. If you know any two, you can find the third.

Distance = Speed × Time; Speed = Distance / Time; Time = Distance / Speed

Distance-Time Graph

A distance-time graph shows how the distance of an object from a starting point changes over time. The horizontal axis (x-axis) represents time, and the vertical axis (y-axis) represents distance. A horizontal line indicates the object is stationary. A sloping line indicates the object is moving, with a steeper line meaning a faster speed. A line sloping upwards means movement away from the starting point, and downwards means movement back towards it.

Real-Life Graphs

Real-life graphs represent relationships between two quantities in everyday situations (e.g., temperature over time, cost of items, growth of a plant). They are used to visualise trends and extract specific information.

Key facts to remember

11 hour = 60 minutes, and 1 minute = 60 seconds.
2Midnight is 00:00 (or 24:00) in 24-hour time. Noon is 12:00.
3The three formulae linking Distance (D), Speed (S), and Time (T) are: D = S × T, S = D / T, T = D / S.
4On a distance-time graph, the x-axis represents time and the y-axis represents distance.
5A horizontal line on a distance-time graph indicates that the object is stationary (not moving).
6A steeper line on a distance-time graph indicates a faster speed.
7Always ensure units are consistent (e.g., km with km/h, hours with km/h) before performing calculations.

Worked examples

Example 1

Convert the following times:\n(a) 7:30 AM to 24-hour time.\n(b) 4:15 PM to 24-hour time.\n(c) 09:40 to 12-hour time.\n(d) 21:05 to 12-hour time.

I(a) 7:30 AM is before noon, so the hour remains the same in 24-hour format.

II(b) 4:15 PM is after noon, so add 12 to the hour for 24-hour format (4 + 12 = 16).

III(c) 09:40 is before 12:00, so it is AM in 12-hour format.

IV(d) 21:05 is after 12:00, so subtract 12 from the hour for 12-hour format (21 - 12 = 9) and add PM.

Answer

(a) 07:30\n(b) 16:15\n(c) 9:40 AM\n(d) 9:05 PM

Remember that 12 AM (midnight) is 00:00 and 12 PM (noon) is 12:00 in 24-hour time.

Example 2

A car travels at an average speed of 80 km/h for 2 hours and 30 minutes. What distance does it cover?

I1. Identify the given values: Speed (S) = 80 km/h, Time (T) = 2 hours 30 minutes.

II2. Convert time to hours only: 30 minutes = 30/60 hours = 0.5 hours. So, T = 2.5 hours.

III3. Choose the correct formula: Distance = Speed × Time (D = S × T).

IV4. Substitute the values and calculate.

Answer

D = 80 km/h × 2.5 h = 200 km

Always ensure your units for speed and time are consistent before calculating.

Example 3

The distance-time graph below shows a person's journey.\n(a) How far did the person travel in the first 2 hours?\n(b) How long did the person stop for?\n(c) Calculate the speed of the person between 3 hours and 5 hours.\n(Assume the graph starts at (0,0), goes to (2, 80), then to (3, 80), and finally to (5, 180).)

I(a) Locate 2 hours on the x-axis and read the corresponding distance on the y-axis.

II(b) Identify the horizontal segment of the graph. This represents the time when the person was stationary. Calculate the duration of this segment.

III(c) For the segment between 3 hours and 5 hours:\n 1. Find the distance at 3 hours and at 5 hours.\n 2. Calculate the distance travelled during this period (change in distance).\n 3. Calculate the time taken during this period (change in time).\n 4. Use the formula Speed = Distance / Time.

Answer

(a) At 2 hours, the distance is 80 km. So, the person travelled 80 km.\n(b) The graph is horizontal between 2 hours and 3 hours. Time stopped = 3 hours - 2 hours = 1 hour.\n(c) At 3 hours, distance = 80 km. At 5 hours, distance = 180 km.\n Distance travelled = 180 km - 80 km = 100 km.\n Time taken = 5 hours - 3 hours = 2 hours.\n Speed = 100 km / 2 h = 50 km/h.

A horizontal line on a distance-time graph means the object is not moving. The gradient (steepness) of the line represents speed.

Common mistakes

✗Confusing 12 AM (midnight, 00:00) with 12 PM (noon, 12:00) when converting between 12-hour and 24-hour clock formats.
✗Not converting units (e.g., using minutes in a calculation where speed is given in km/h) before applying formulae.
✗Incorrectly applying the distance, speed, time formulae (e.g., calculating speed as Time / Distance).
✗Misinterpreting a horizontal line on a distance-time graph as constant speed instead of being stationary.
✗Reading the wrong axis or misinterpreting the scale on any type of graph.

Exam tips

★Draw the 'DST triangle' (Distance at the top, Speed and Time at the bottom) to help remember the formulae for distance, speed, and time.
★Always write down the formula you are using before substituting values into it.
★Carefully check the units given in the question and ensure your final answer has the correct units. Convert units if necessary at the start of the problem.
★When interpreting graphs, read the axes labels and scales carefully to avoid errors.
★Use a ruler and a sharp pencil for drawing and reading values from graphs to ensure accuracy.

Ready to practise?

Try a problem on this topic

Snap a photo or type a question — get step-by-step working instantly.

Solve a problem →← Maths curriculum