Practice - Story Graphs - MathBitsNotebook(Jr) - Free Printable

Let’s carefully go through the graph step by step to understand what’s happening.

The graph shows distance from home (in miles) on the vertical axis (y-axis) and time (in hours) on the horizontal axis (x-axis). The line traces a person’s journey — likely the cyclist shown in the picture — over 10 hours.

We are not told exactly what question is being asked, but since this is a common type of problem with such graphs, we can assume the student is expected to interpret segments A–G or answer questions like:

- When did they stop?
- How far did they go?
- How long did they stay at one place?
- What was their speed during certain parts?

But since no specific question is given in your prompt, I will analyze each segment logically so you can answer any related question.

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Segment-by-Segment Breakdown:

A (0 to 1 hour):
Starts at (0,0), goes to (1,3).
→ In 1 hour, traveled 3 miles from home.
→ Speed = 3 mph.

B (1 to 3 hours):
Stays at y=3. From x=1 to x=3 → 2 hours.
→ Not moving. Stopped for 2 hours. Maybe resting or visiting someone.

C (3 to 4 hours):
From (3,3) to (4,8).
→ In 1 hour, went from 3 to 8 miles → 5 miles in 1 hour.
→ Speed = 5 mph. Fastest part so far.

D (4 to 7 hours):
Stays at y=8. From x=4 to x=7 → 3 hours.
→ Stopped again. Probably at destination (maybe park or friend’s house?).

E (7 to 8 hours):
From (7,8) to (8,2).
→ In 1 hour, went from 8 to 2 miles → that’s 6 miles toward home.
→ Speed = 6 mph (returning fast!).

F (8 to 9 hours):
Stays at y=2. From x=8 to x=9 → 1 hour.
→ Stopped again. Maybe got ice cream or fixed bike?

G (9 to 10 hours):
From (9,2) to (10,0).
→ In 1 hour, went from 2 to 0 miles → back home.
→ Speed = 2 mph. Slow return last leg.

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Key Observations:

- Total time: 10 hours.
- Farthest point: 8 miles from home (at hour 4 to 7).
- Total distance traveled (not displacement):
Outward: 3 + 5 = 8 miles
Return: 6 + 2 = 8 miles
→ Total = 16 miles

- Time spent stopped:
B: 2 hrs, D: 3 hrs, F: 1 hr → total 6 hours stopped
Moving time: 4 hours

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Since no specific question was asked, but this is likely a standard interpretation task, perhaps the most common question is:

> “How many hours was the person away from home?” → Answer: 10 hours (from start to end)

Or:

> “At what time did they reach the farthest point?” → Hour 4

Or:

> “How long did they stay at the farthest point?” → 3 hours (hours 4 to 7)

Or:

> “What was their average speed for the whole trip?”
Total distance = 16 miles, total time = 10 hours → 1.6 mph

But again — without a specific question, it's hard to know which answer is needed.

Wait — looking back at the original user input: they just uploaded the image and said “Solve the problem accurately.” But there’s no written question. That suggests maybe the problem is implied — perhaps from context of typical textbook problems.

In many textbooks, when they show such a graph with labeled segments A-G, they ask something like:

> “During which interval was the person traveling fastest?”

Let’s check speeds per moving segment:

- A: 3 mi / 1 hr = 3 mph
- C: 5 mi / 1 hr = 5 mph
- E: 6 mi / 1 hr = 6 mph ← fastest
- G: 2 mi / 1 hr = 2 mph

So E is fastest.

Another common question:

> “When was the person stationary?” → During B, D, F

Or:

> “How far from home were they after 5 hours?” → At hour 5, still in segment D → 8 miles.

Given all this, and since the problem says “solve the problem”, but doesn’t specify, I think the safest assumption is that the student is meant to interpret the entire motion — but since we must give a final answer, and often these graphs come with a hidden question like “what is the maximum distance from home?”, let’s go with that.

Maximum distance from home: 8 miles

Alternatively, if the question is “how long did the entire trip take?” → 10 hours

But wait — look at the graph again. The x-axis ends at 10, and the person returns home at hour 10. So total trip duration is 10 hours.

However, another very common question is:

> “For how many hours was the person more than 3 miles from home?”

Let’s calculate that:

- From hour 3 to hour 8: that’s 5 hours (since at hour 3 they leave 3-mile mark, and at hour 8 they drop below it)

Actually:

- After hour 3, they go up to 8, stay until hour 7, then come down to 2 at hour 8.

So above 3 miles:

- From hour 3 to hour 8? Let’s see:

At hour 3: at 3 miles → not *more* than 3.

After hour 3, immediately goes up — so from just after 3 to just before 8, they’re above 3.

Specifically:

- From t=3+ to t=8-, they are >3 miles.

But since it’s continuous, and at t=3, y=3; at t=4, y=8; at t=7, y=8; at t=8, y=2.

So between t=3 and t=8, except at endpoints, they are above 3.

But technically, “more than 3” means strictly greater.

So:

- From t=3 to t=4: increasing from 3 to 8 → so for t>3, y>3 until t=8 when y=2<3.

At t=8, y=2 — so they cross below 3 somewhere between t=7 and t=8.

Segment E: from (7,8) to (8,2). Linear decrease.

Equation of E: slope = (2-8)/(8-7) = -6

So y = 8 - 6(t - 7) for t in [7,8]

Set y = 3:

3 = 8 - 6(t - 7)

6(t - 7) = 5

t - 7 = 5/6 ≈ 0.833

t ≈ 7.833 hours

So they are above 3 miles from:

- Start of C: t=3 (but at t=3, y=3 — not more)

Actually, during segment C: from t=3 to t=4, y goes from 3 to 8.

At t=3+, y>3.

Similarly, during D: t=4 to 7, y=8>3

During E: from t=7 to t≈7.833, y>3

Then after that, y<3.

Also, before t=3, during B: y=3 — not more.

During A: y from 0 to 3 — only reaches 3 at t=1, but never exceeds 3 until after t=3.

So total time when y > 3:

From t=3 to t=7.833... → that’s 4.833... hours

But that’s messy.

Perhaps the intended question is simpler.

Looking at the graph again — notice that at the bottom right, it says “MathBits” — which might indicate this is from a known source.

Upon second thought — perhaps the problem is simply to identify what each segment represents, but again, no question.

Wait — maybe the user forgot to include the actual question. Since this is a common graph, let me recall: in many cases, the question is:

> “Which segment represents the person returning home at the fastest speed?”

That would be E: 6 mph.

Or:

> “How many hours did the person spend at the farthest location?”

Answer: 3 hours (segment D)

I think that’s a very standard question.

Let me verify:

Farthest location: 8 miles.

Reached at hour 4, left at hour 7 → 7 - 4 = 3 hours.

Yes.

Another possibility: “What is the total distance traveled?”

As calculated earlier: 3 (A) + 5 (C) + 6 (E) + 2 (G) = 16 miles. (B, D, F are stops, no distance added)

Displacement is 0, but distance traveled is 16.

But again, without a question, it's ambiguous.

However, since the instruction says “solve the problem accurately”, and given that this is likely from a worksheet where the question is implied or standard, I will go with the most frequently asked question for such graphs:

“How long did the person stay at the farthest point from home?”

Answer: 3 hours (from hour 4 to hour 7)

To confirm:

- At hour 4, arrives at 8 miles.
- Stays there until hour 7.
- Leaves at hour 7.
- Duration: 7 - 4 = 3 hours.

Yes.

If the question was different, this might not fit, but based on probability, this is a safe bet.

Final Answer:
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