Distance-Time Graphs Worksheet | PDF Printable Algebra Worksheet - Free Printable

Let’s solve each question step by step.

---

## 1) Calculate the average speed of the journey represented by each line in the following diagrams.

Average speed = Total Distance ÷ Total Time

---

First Graph (Distance in km, Time in hours)

- At time = 4 hours, distance = 200 km
- Speed = 200 km ÷ 4 h = 50 km/h

✔ Answer: 50 km/h

---

Second Graph (Distance in meters, Time in seconds)

- At time = 20 seconds, distance = 400 m
- Speed = 400 m ÷ 20 s = 20 m/s

✔ Answer: 20 m/s

---

Third Graph (Distance in miles, Time in hours)

- At time = 2 hours, distance = 18 miles (approximate from graph — it’s just under 20, and grid lines suggest 18)
- *Note: If we count carefully, at 2 hours, the line is at 18 miles (each grid square = 2 miles; 9 squares up).*
- Speed = 18 miles ÷ 2 h = 9 miles/hour

✔ Answer: 9 mph

*(If the graph shows exactly 18 miles at 2 hours, then 9 mph is correct. Some might interpret it as 17 or 19, but 18 is most accurate based on grid.)*

---

## 2) Jameka went for a walk. Her walk is represented by the graph.

a. Describe the part of her walk represented by sections CD, DE, and EF.

- CD: From point C (time=4h, distance=12km) to D (time=5h, distance=6km) → She is walking back towards home (distance decreasing), covering 6 km in 1 hour.
- DE: From D (time=5h, distance=6km) to E (time=6h, distance=6km) → She is stationary (no change in distance).
- EF: From E (time=6h, distance=6km) to F (time=8h, distance=0km) → She is walking back home, covering 6 km in 2 hours.

✔ Answers:
- CD: Walking back toward home at a steady pace.
- DE: Standing still / resting.
- EF: Walking slowly back home.

---

b. On which section of the walk did she walk fastest?

Speed = Distance ÷ Time → Steeper slope = faster speed.

Compare slopes:

- AB: From (0,0) to (3,12) → 12 km in 3 h → 4 km/h
- BC: Horizontal → 0 km/h (resting)
- CD: 6 km in 1 h → 6 km/h
- DE: Horizontal → 0 km/h
- EF: 6 km in 2 h → 3 km/h

✔ Fastest section: CD (6 km/h)

---

c. What was her average speed for the first 2 hours?

From graph:
- At t=0, distance=0
- At t=2, distance=8 km (since AB goes from (0,0) to (3,12), so at t=2, it’s 8 km — because 12 km over 3 hours = 4 km/h → 2×4=8 km)

Average speed = 8 km ÷ 2 h = 4 km/h

✔ Answer: 4 km/h

---

## 3) The graph represents the journey of a steam train.

a. How far did the train travel in the first 40 minutes?

Look at graph at time = 40 minutes:

- Point C is at 40 minutes, distance = 10 km

But wait — from A to B (0–30 min): distance increases to 10 km
From B to C (30–40 min): distance stays at 10 km → so total distance traveled is still 10 km

✔ Answer: 10 km

*(Note: “How far did the train travel” usually means total distance covered, not displacement. Since it didn’t move between 30–40 min, total distance remains 10 km.)*

---

b. Work out the speed of the train between A and B. Give your answer in km per hour.

A to B: from (0,0) to (30 min, 10 km)

Time = 30 minutes = 0.5 hours
Distance = 10 km

Speed = 10 km ÷ 0.5 h = 20 km/h

✔ Answer: 20 km/h

---

c. What does the line DE represent?

D is at (50 min, 20 km), E is at (90 min, 0 km)

→ Distance is decreasing from 20 km to 0 km → Train is returning to station.

Slope is constant → constant speed.

So, DE represents the train returning to the station at a steady speed.

✔ Answer: The train is returning to the station at a constant speed.

---

## ✔ Final Answers Summary:

1) Average speeds:

- First graph: 50 km/h
- Second graph: 20 m/s
- Third graph: 9 mph

2) Jameka’s walk:

- a.
- CD: Walking back toward home
- DE: Resting/stationary
- EF: Walking slowly back home
- b. CD (fastest)
- c. 4 km/h

3) Steam train:

- a. 10 km
- b. 20 km/h
- c. Train returning to station at constant speed

Let me know if you’d like these explained with diagrams or visual annotations!