Question

toms journey is shown on the distance-time graph below.
he travelled the final 3 hours of his journey at a constant speed of \\(80\text{ km/h}\\).
work out the value of \\(d\\).

Explanation:

Identify the given values from the graph

From the distance-time graph, we can identify the key coordinates and intervals:

• At \(t = 0\), the distance is \(0\text{ km}\).
• At \(t = 2\text{ hours}\), the distance is \(180\text{ km}\).
• From \(t = 2\text{ hours}\) to \(t = 3\text{ hours}\), the distance remains constant at \(180\text{ km}\) (Tom is stationary).
• The final part of the journey starts at \(t = 3\text{ hours}\) and ends at \(t = 6\text{ hours}\).
• The total duration of this final section is:

$$ \Delta t = 6 - 3 = 3\text{ hours} $$

• The distance at the start of this final section (\(t = 3\)) is \(180\text{ km}\).
• The distance at the end of this final section (\(t = 6\)) is \(d\text{ km}\).

Apply the constant speed formula

We are given that Tom travelled the final 3 hours of his journey at a constant speed of \(80\text{ km/h}\).
The formula relating speed, distance, and time is:

$$ \text{Speed} = \frac{\Delta \text{Distance}}{\Delta \text{Time}} $$

Substituting the known values into the formula:

$$ 80 = \frac{d - 180}{3} $$

Solve for the unknown value d

Multiply both sides of the equation by 3 to isolate the distance term:

$$ 80 \times 3 = d - 180 $$

$$ 240 = d - 180 $$

Add 180 to both sides to find \(d\):

$$ d = 240 + 180 $$

$$ d = 420 $$

Answer:

Work out the value of d.
\(d =\) <blank>420</blank>