Level 4

Create and interpret graphs involving time

Lesson

Travel graphs are line graphs that are used to describe the motion of objects such as cars, trains, cyclists or people. In other words, we use travel graphs to show journeys.

We can gather a lot of information from travel graphs, so it is important that we understand the different components. The distance travelled is represented on the vertical axis and the time taken to travel that distance is represented on the horizontal axis. The steepness of the line indicates the speed at which the object is travelling. The steeper the line, the faster the object is travelling.

Remember!

$\text{speed }=\frac{\text{distance }}{\text{time }}$speed =distance time

Graphs showing one person's journey

We can think of the horizontal axis as the starting point of the journey. The further the line moves away from the horizontal axis, the further we are away from the starting point. When the line runs horizontally, it indicates a rest or a break. In other words, the person has stopped so the distance isn't changing.

Let's say Bob recorded his distance from his home for nine minutes and his results are displayed in the graph above. We can see in the graph above that initially Bob was $1$1 km away from his house and he reached home $1$1 minute later. He stayed home for one minute (indicated by the straight line along the horizontal axis), then left a minute later. He travelled for two minutes until he was $4$4 km away from home. Then Bob stopped for another $2$2 minutes before he returned home, which took him another $3$3 minutes. We know Bob is home because the line finishes on the horizontal axis.

A graph showing two different journeys

The next graph shows two different journeys. You can see that there is a difference with the steepness of the lines drawn. Remember that, the steeper the line, the faster the average speed. We can calculate the average speeds, by reading distances from the graph, and dividing by the time taken.

You will also notice from the graph that the two lines cross. This means that the two boys were the same distance away at the same time. Since they were the same distance away for an hour, it may indicate that they met up.

Remember!

A graph showing a journey (or journeys) should have time on the horizontal axis, and distance from somewhere on the vertical axis.
A line moving up away from the horizontal axis shows a journey moving away from the starting place.
A line moving down towards the horizontal axis shows a journey returning back towards the starting place.
A horizontal line is a break or rest. In other words, the person isn't moving.
The intersection point of two lines indicates two people are the same distance away from the starting point- maybe they met up.

Worked Examples

Question 1

The graph shown describes $Frank$ 's distance from home throughout his journey.

	Distance From Home
Distance(km)	Loading Graph... A Cartesian graph titled Distance From Home is displayed with the horizontal axis labeled Time (am) and the vertical axis labeled Distance (km). A piecewise linear graph is plotted in the Cartesian graph. The first point is located at $coord(5, 5)$ . Second point at $coord(6, 15)$ . Third point at $coord(7, 30)$ . Fourth point at $coord(8, 30)$ . Fifth point at $coord(9, 40)$ . And the last point at $coord(10, 50)$ . The coordinates are not explicitly shown on the graph.
	Time (am)

How far was $Frank$ from home when he started driving at $5$5 am?
How far was he from home by $7$7 am?
How long did he take to rest?
How far did he travel between $7$7 am and $9$9 am?
Was $Frank$ travelling faster in the first two hours (between $5$5 am and $7$7 am) or the last two hours (between $8$8 am and $10$10 am) of his trip?
First two hours
A
Last two hours
B

QUESTION 2

A husband and wife transport medical equipment from their respective work sites throughout the day. The graph shows their distance from home.

A line graph is displayed with the horizontal axis labeled "Time" marked from 10am to 6pm at 1-hour increment. The vertical axis labeled "Distance(km)" marked from 0 to 350 at increments of 50. Two lines are plotted to represent the distance from home of a husband named Sourav and wife named Irena. The blue line represents Sourav's distance over time, and the red line represents Irena's distance over time. The blue line is made up of four line segments connecting several points, starting from 100 km at 10:00 am, to 200 km at 11:00 am, to 250 km at 12:30 pm, to 250 km at 1:30 pm and drops to 100 km at 4:30 pm. The red line is made up of five line segments connecting several points, starting from 300 km at 10:00 am, drops to 150 km at 11:30 am, to 100 km at 1:00 pm, to 150 km at 2:30 pm, to 150 km at 3:30 pm and to 300 km at 5:30 pm. The location of each point is not explicitly labeled in the graph.

If they are at their respective worksites at the beginning of the day, how far apart are their worksites? Assume the distances are in the same direction.
At what time are both Sourav and Irena the same distance away from their respective work sites?
$1$1 pm
A
$3:30$3:30 pm
B
$11$11 am
C
How far apart are they at $1$1 pm?
How far apart are they when Sourav is returning to his office and is $25$25 km from it?
$150$150 km
A
$50$50 km
B
$62.5$62.5 km
C
$0$0 km
D
How long after Sourav returned to his worksite did Irena return to hers?
$1$1 hour
A
$\frac{1}{2}$12 an hour
B
$2$2 hours
C

Outcomes

S4-1

Plan and conduct investigations using the statistical enquiry cycle:– determining appropriate variables and data collection methods;– gathering, sorting, and displaying multivariate category, measurement, and time-series data to detect patterns, variations, relationships, and trends;– comparing distributions visually;– communicating findings, using appropriate displays.