Speed-Distance-Time Graph Analysis Problems worksheet | Live ... - Free Printable

Let’s solve each question step by step, using the graphs provided.

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Question 1: Class 8A’s journey to the zoo

We are looking at a distance-time graph. The vertical axis shows “Distance from school (miles)”, and the horizontal axis shows “Time of day”.

The line goes up when they’re moving away from school, flat when stopped, and steeper = faster speed.

(a) What time did the bus leave school?
→ Look at where the line starts rising from 0 miles. That’s at 09:00.

(b) What time did they stop for a picnic?
→ The line becomes flat — that means they stopped. It flattens at 10:00.

(c) How far had they travelled when they stopped for a picnic?
→ At 10:00, the distance is 50 miles (look at the y-axis value where the line flattens).

(d) How long did they stop for?
→ The flat part lasts from 10:00 to 10:30 → that’s 30 minutes.

(e) What time did they arrive at the zoo?
→ The line stops going up at the end — that’s arrival. It ends at 11:30.

(f) How far is the zoo from school?
→ At 11:30, the distance is 90 miles (top point on the graph).

✔ Double-check: From 09:00 to 10:00 → 50 miles in 1 hour. Then stop 30 min. Then from 10:30 to 11:30 → another 40 miles in 1 hour. Total = 90 miles. Makes sense.

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Question 2: Emma’s trip to Grandma’s house and back

This graph also shows distance from home over time. When the line goes up → she’s going away. Flat → staying still. Going down → coming back home.

(a) What time did Emma begin her journey?
→ Line starts rising at 7:30 am (halfway between 7am and 8am).

Wait — let’s check the graph carefully. The x-axis has marks at 7am, 8am, 9am, etc. Each big square is 1 hour. Between 7am and 8am, there are 2 small squares → so each small square = 30 minutes.

The line starts at the first small square after 7am → that’s 7:30 am.

But wait — actually, looking again: the red line starts exactly at 7:30? Let me recheck.

Actually, in many such graphs, if it starts halfway between 7 and 8, it’s 7:30. But let’s look at the grid:

From 7am to 8am → 2 boxes → each box = 30 min.

The line starts at the very beginning of the first box after 7am → that’s 7:30 am.

BUT — hold on! In some versions, it might start at 7:00. Let me think again.

Looking at the graph description: the line starts at 7am? No — the line starts at the origin? Wait, no — the y-axis starts at 0, but the x-axis starts at 7am.

Actually, in the graph, the red line begins at 7:30 am, because it starts halfway between 7am and 8am.

Wait — I need to be precise.

Let me count the grid:

- X-axis: from 7am to 8am → divided into 2 equal parts → each part = 30 minutes.
- The red line starts at the first tick after 7am → that’s 7:30 am.

But let’s confirm with other points.

At 8am, she is at 20 miles? Let’s see.

Actually, let’s read the graph properly.

At 8am → distance = 20 miles? No — at 8am, the line is at 20? Wait, no.

Look: at 8am, the line is at 20 miles? Actually, from 7:30 to 8:30, she goes from 0 to 40 miles? Let’s calculate slope.

Better approach: find key points.

The line rises from (7:30, 0) to (8:30, 40)? Wait, no.

Actually, looking at the graph:

- At 8am → distance = 20 miles? Or 40?

I think I made a mistake.

Let me reinterpret based on standard graph reading.

In Question 2 graph:

- Y-axis: Distance from home (miles), from 0 to 50.
- X-axis: Time, from 7am to 12 noon. Each major grid line is 1 hour. Between them, 2 minor grids → so each minor grid = 30 minutes.

Now, the red line:

- Starts at 7:30 am (first minor grid after 7am) at 0 miles.
- Goes up to 8:30 am at 40 miles? Wait, at 8:30 am, it reaches 40 miles? Let's see.

Actually, at 8am, the line is at 20 miles? Because from 7:30 to 8:30 is 1 hour, and if it goes to 40 miles, then at 8am (halfway) it should be 20 miles. Yes.

Then it stays flat from 8:30 am to 10:00 am at 40 miles.

Then goes down from 10:00 am to 12:00 noon, reaching 0 at 12:00.

But let’s answer questions one by one.

(a) What time did Emma begin her journey?
→ The line starts rising at 7:30 am.

(b) How far was Emma from home at 8am?
→ At 8am, which is halfway between 7:30 and 8:30. Since she went from 0 to 40 miles in 1 hour (from 7:30 to 8:30), at 8am (30 min into trip), she’d be at 20 miles. So 20 miles.

(c) How long did Emma stay at her Grandmother’s house?
→ She stays where the line is flat. Flat from 8:30 am to 10:00 am → that’s 1 hour 30 minutes.

(d) What time did Emma leave her Grandmother’s house?
→ The line starts going down at 10:00 am.

(e) How far was Emma from home at 11:45?
→ 11:45 is 15 minutes before 12:00. From 10:00 to 12:00, she travels back 40 miles in 2 hours → speed = 20 mph.

So in last 15 minutes (which is 0.25 hours), she covers 20 * 0.25 = 5 miles. So at 11:45, she is 5 miles from home? Wait, no — she’s coming back, so distance from home is decreasing.

At 12:00, she’s at 0. At 11:45, 15 min before, she has 5 miles left to go → so she is 5 miles from home.

Alternatively, from 10:00 to 11:00: she goes from 40 to 30 miles? Let’s see the graph.

Actually, looking at the graph: at 11am, she is at 30 miles? And at 12pm, 0 miles.

From 10am to 12pm: 2 hours, 40 miles → 20 mph.

At 11:45, which is 1.75 hours after 10am? No — from 10am to 11:45 is 1 hour 45 min = 1.75 hours.

Distance covered in return: 20 mph * 1.75 h = 35 miles. So she has 40 - 35 = 5 miles left → so 5 miles from home.

Yes.

(f) How far did Emma travel in total?
→ She went 40 miles to Grandma’s, then 40 miles back → total 80 miles.

✔ Double-check: Outward: 40 miles. Return: 40 miles. Total 80. Correct.

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Final Answer:

Question 1:
(a) 09:00
(b) 10:00
(c) 50 miles
(d) 30 minutes
(e) 11:30
(f) 90 miles

Question 2:
(a) 7:30 am
(b) 20 miles
(c) 1 hour 30 minutes
(d) 10:00 am
(e) 5 miles
(f) 80 miles