Distance-time graph illustrating Emma's journey with five stages; evaluate the truth of statements about her travel speed, distance, and stops.

Let's analyze Emma's Journey using the distance-time graph and evaluate each statement as True or False.

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📈 Understanding the Graph

- Y-axis: Distance from home (in km)
- X-axis: Time (in minutes)
- The journey is divided into 5 stages, labeled 1 to 5.

We'll go through each stage:

#### Stage 1 (0–15 min):
- Starts at (0, 0), ends at (15, 5)
- Distance = 5 km in 15 minutes
- Speed = $ \frac{5}{15} = \frac{1}{3} $ km/min ≈ 20 km/h

#### Stage 2 (15–30 min):
- Horizontal line: distance stays at 5 km
- So Emma is stationary

#### Stage 3 (30–40 min):
- From (30, 5) to (40, 3)
- Distance decreases by 2 km over 10 minutes
- Moving back toward home
- Speed = $ \frac{2}{10} = 0.2 $ km/min = 12 km/h (but direction is reverse)

#### Stage 4 (40–55 min):
- From (40, 3) to (55, 7)
- Distance increases from 3 km to 7 km → 4 km
- Time = 15 minutes
- Speed = $ \frac{4}{15} $ km/min ≈ 16 km/h

#### Stage 5 (55–60 min):
- Horizontal line at 7 km
- Stationary again

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Now let’s evaluate each statement.

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✔ A. During stage 1, Emma travelled at 3 km/minute.

- False
- In stage 1: 5 km in 15 minutes → speed = $ \frac{5}{15} = \frac{1}{3} $ km/min ≈ 0.333 km/min
- 3 km/minute is extremely fast (that’s 180 km/h!)
- So this is false

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✔ B. Emma was stationary during stage 2.

- True
- The graph is flat (horizontal) between 15 and 30 minutes → no change in distance
- So she is not moving

✔ True

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✔ C. The graph shows that Emma reached the top of two hills.

- This is ambiguous, but let's interpret:
- "Top of a hill" likely means maximum distance from home.
- She reaches 5 km at stage 2 → one peak
- Then goes down to 3 km, then up to 7 km → second higher peak
- So she reaches two local maxima? But only one absolute maximum at 7 km
- However, “top of two hills” could mean two peaks in her journey.
- But she only reaches one high point (at 7 km) — before that, she went to 5 km, then came down, then went up.
- But since she didn’t go *higher* than 5 km until later, we can say:
- First peak: 5 km (stage 2)
- Second peak: 7 km (end of stage 4)
- So yes, two peaks — two times she reached a high point.
- So it's reasonable to say she reached the top of two hills.

✔ True

> Note: Some might argue it’s just one hill with a dip, but given the wording, it’s acceptable to consider both peaks.

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✔ D. Emma travelled 4000m during Stage 4.

- Stage 4: from 3 km to 7 km → distance = 4 km = 4000 meters
- Yes, so she traveled 4000 m.

✔ True

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✔ E. The slowest part of Emma’s journey was during stage 3.

- Let’s compare speeds:

| Stage | Distance (km) | Time (min) | Speed (km/min) |
|-------|----------------|------------|----------------|
| 1 | 5 | 15 | 0.333 |
| 2 | 0 | 15 | 0 |
| 3 | 2 | 10 | 0.2 |
| 4 | 4 | 15 | 0.267 |

But wait — Stage 2 has zero speed → she's stationary → slowest possible
- Stage 3: 0.2 km/min = 12 km/h
- Stage 2: 0 km/min → slower than stage 3

So stage 2 is slower than stage 3.

Therefore, E is false — stage 3 is not the slowest.

✘ False

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✔ F. Emma’s average speed over the whole journey was 7 km/h.

- Total distance = final distance – start = 7 km – 0 km = 7 km
- Total time = 60 minutes = 1 hour
- Average speed = $ \frac{7 \text{ km}}{1 \text{ h}} = 7 \text{ km/h} $

✔ True

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✔ G. Emma was travelling faster during stage 4 than stage 1.

- Stage 1: 5 km / 15 min = $ \frac{1}{3} $ km/min ≈ 0.333 km/min
- Stage 4: 4 km / 15 min = $ \frac{4}{15} \approx 0.267 $ km/min

So stage 1 was faster than stage 4.

✘ False

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✔ H. When she was 5 minutes into her journey, Emma had travelled 3 km.

- At 5 minutes, look at the graph:
- Stage 1 is linear from (0,0) to (15,5)
- So slope = $ \frac{5}{15} = \frac{1}{3} $
- At 5 min: distance = $ \frac{1}{3} \times 5 = \frac{5}{3} \approx 1.67 $ km
- Not 3 km

✘ False

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✔ Final Answers:

True Statements:
B, C, D, F

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✔ Summary:

| Statement | True/False | Reason |
|---------|------------|--------|
| A | ✘ False | Speed was ~0.333 km/min, not 3 |
| B | ✔ True | Flat line → stationary |
| C | ✔ True | Two peaks: 5 km and 7 km |
| D | ✔ True | 4 km = 4000 m |
| E | ✘ False | Stage 2 (0 km/min) was slower than stage 3 |
| F | ✔ True | 7 km in 1 hour = 7 km/h |
| G | ✘ False | Stage 1 faster than stage 4 |
| H | ✘ False | At 5 min, only ~1.67 km |

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✔ Answer:

True Statements: B, C, D, F