Questions: A boat travels a total distance of 150 km in a time of 20 hours. iii Calculate the average speed of the boat. iv For more than half of the time that the boat was travelling, its speed was 12 km/h. Explain the difference between this speed and your answer to (part i). [Total: 6]

A boat travels a total distance of 150 km in a time of 20 hours. iii Calculate the average speed of the boat. iv For more than half of the time that the boat was travelling, its speed was 12 km/h. Explain the difference between this speed and your answer to (part i). [Total: 6]
Transcript text: d A boat travels a total distance of 150 km in a time of 20 hours. iii Calculate the average speed of the boat. [2] $\qquad$ $\qquad$ iv For more than half of the time that the boat was travelling, its speed was $12 \mathrm{~km} / \mathrm{h}$. Explain the difference between this speed and your answer to (part $\mathbf{i}$ ). [2] $\qquad$ $\qquad$ [Total: 6]
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Solution

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Solution Steps

Step 1: Calculate the Average Speed of the Boat

The average speed of the boat can be calculated using the formula for average speed:

\[ \text{Average speed} = \frac{\text{Total distance}}{\text{Total time}} \]

Given:

  • Total distance = 150 km
  • Total time = 20 hours

Substitute the given values into the formula:

\[ \text{Average speed} = \frac{150 \text{ km}}{20 \text{ hours}} = 7.5 \text{ km/h} \]

Step 2: Explain the Difference Between the Given Speed and the Average Speed

The problem states that for more than half of the time, the boat was traveling at a speed of \(12 \text{ km/h}\). This means that for the remaining time, the boat must have been traveling at a speed lower than \(7.5 \text{ km/h}\) to bring the overall average speed down to \(7.5 \text{ km/h}\).

The average speed is a weighted average of the different speeds the boat traveled at different times. Since the boat traveled at \(12 \text{ km/h}\) for more than half of the time, it must have traveled at a significantly lower speed for the remaining time to achieve an overall average speed of \(7.5 \text{ km/h}\).

Final Answer

\[ \boxed{\text{Average speed} = 7.5 \text{ km/h}} \]

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