Here are the solutions to the problems on the worksheet.
1) Work out the average speed
To find the average speed, we use the formula:
$$ \text{Speed} = \frac{\text{Distance}}{\text{Time}} $$
*
First Graph (Left):
* The line goes up to
200 km in
4 hours.
* Calculation: $200 \div 4 = 50$
* Answer:
50 km/h
*
Second Graph (Middle):
* The line goes up to
400 m in
20 seconds.
* Calculation: $400 \div 20 = 20$
* Answer:
20 m/s
*
Third Graph (Right):
* The line goes up to
16 miles in
2 hours. (Looking at the grid, the point at 2 hours is 3 small squares above 10. Each square is 2 units, so $10 + 6 = 16$).
* Calculation: $16 \div 2 = 8$
* Answer:
8 mph
---
2) Jameka’s Walk
a. Describe the sections CD, DE, and EF:
*
Section CD: The line is flat (horizontal). This means time is passing, but the distance isn't changing. Jameka has
stopped or is resting.
*
Section DE: The line goes down. This means the distance from home is getting smaller. Jameka is
walking back towards home.
*
Section EF: The line continues to go down until it hits the bottom axis (distance = 0). She continues walking back and
arrives home.
b. On which section did she walk fastest?
* Speed is shown by how steep the line is. The steeper the line, the faster the speed.
* Comparing the slopes:
* AB: Goes up 12 km in 3 hours ($4$ km/h).
* DE: Goes down 6 km (from 12 to 6) in 1 hour ($6$ km/h).
* EF: Goes down 6 km (from 6 to 0) in 3 hours ($2$ km/h).
* The steepest part is
DE.
c. Average speed for the first 2 hours:
* At 2 hours, look at the graph to see how far she walked. The line is at
8 km.
* Calculation: $\frac{8 \text{ km}}{2 \text{ hours}} = 4$
* Answer:
4 km/h
---
3) Steam Train Journey
a. How far did the train travel in the first 40 minutes?
* Look at the horizontal axis (time) for 40 minutes. Follow the line up to the graph.
* The graph is at point C, which lines up with
10 km on the vertical axis.
* Answer:
10 km
b. Speed of the train between A and B:
*
Distance: From A (0) to B (10 km), the train traveled
10 km.
*
Time: From A (0) to B (30 mins), it took
30 minutes.
* To get km per
hour, we need to convert the time. 30 minutes is half an hour ($0.5$ hours).
* Calculation: $\frac{10 \text{ km}}{0.5 \text{ hours}} = 20$
* Answer:
20 km/h
c. What does the line DE represent?
* The line goes downwards from a high distance (20 km) back to zero distance (the station).
* This represents the train
returning to the station.
──────────────────────────────────────
Final Answer:
1) Average Speeds:
* Left Graph:
50 km/h
* Middle Graph:
20 m/s
* Right Graph:
8 mph
2) Jameka's Walk:
* a.
CD: Stopped/Resting.
DE: Walking back towards home.
EF: Continuing to walk back until arriving home.
* b.
Section DE
* c.
4 km/h
3) Steam Train:
* a.
10 km
* b.
20 km/h
* c.
The train returning to the station.
Parent Tip: Review the logic above to help your child master the concept of time distance worksheet.
