Road Roller Length Levelled

The question asks us to find the length of the road that a cylindrical road roller will level in a specific time, given its speed. The length of the road levelled is essentially the distance covered by the road roller.

We are given the following information:

• Diameter of the road roller = 1.5 m
• Speed of the road roller = 3 km/h
• Time taken = 45 minutes

To find the distance covered (which is the length of the road levelled), we can use the formula:

$\text{Distance} = \text{Speed} \times \text{Time}$

Before we apply the formula, we need to ensure that the units of speed and time are consistent. The speed is given in kilometers per hour (km/h), and the time is given in minutes. Let's convert the time from minutes to hours.

There are 60 minutes in 1 hour. So, to convert minutes to hours, we divide the number of minutes by 60.

$\text{Time in hours} = \frac{\text{Time in minutes}}{60}$

Substituting the given time:

$\text{Time} = \frac{45 \text{ minutes}}{60 \text{ minutes/hour}} = \frac{45}{60} \text{ hours}$

We can simplify the fraction $\frac{45}{60}$:

$\frac{45}{60} = \frac{15 \times 3}{15 \times 4} = \frac{3}{4} \text{ hours}$

So, the time taken is $\frac{3}{4}$ hours, or 0.75 hours.

Now we can calculate the distance (length of the road levelled) using the speed and the converted time:

$\text{Distance} = \text{Speed} \times \text{Time}$

$\text{Distance} = (3 \text{ km/h}) \times (0.75 \text{ hours})$

$\text{Distance} = 3 \times 0.75 \text{ km}$

$\text{Distance} = 2.25 \text{ km}$

Thus, the length of the road levelled in 45 minutes is 2.25 km.

The diameter of the road roller (1.5 m) is additional information in this particular problem, as the total distance covered is directly calculated from the given speed and time. This information would be useful if the question asked about the number of rotations the roller makes.

Let's review the steps:

• Identify the given speed and time.
• Convert time units to match speed units (minutes to hours).
• Use the formula Distance = Speed $\times$ Time to calculate the length levelled.

The calculated length of the road levelled is 2.25 km.