Understanding Cyclist Speed and Distance Calculation

This problem involves calculating the distance a cyclist covers based on a given speed and time. We are provided with the initial distance and time to determine the cyclist's speed. Then, we use this speed to find the distance covered over a different time period, ensuring the final answer is in kilometers.

Step-by-Step Solution to the Cyclist Problem

1. Identify the Given Information

• Initial distance covered by the cyclist: 500 m
• Initial time taken by the cyclist: 5 minutes
• New time duration: Half an hour

2. Convert New Time to Consistent Units

The new time duration is half an hour. We should convert this to minutes to match the unit of the initial time (5 minutes) or convert the initial time and speed to hours. Let's convert half an hour to minutes:

Half an hour = 30 minutes

3. Calculate the Cyclist's Speed

Speed is defined as the distance covered per unit of time. The formula for speed is:

\(\text{Speed} = \frac{\text{Distance}}{\text{Time}}\)

Using the initial information:

\(\text{Speed} = \frac{500 \text{ m}}{5 \text{ minutes}}\)

\(\text{Speed} = 100 \text{ m/minute}\)

So, the cyclist travels at a speed of 100 meters per minute.

4. Calculate the Distance Covered in Half an Hour (30 minutes)

Now that we know the speed, we can calculate the distance covered in 30 minutes using the formula:

\(\text{Distance} = \text{Speed} \times \text{Time}\)

Using the calculated speed and the new time:

\(\text{Distance} = 100 \text{ m/minute} \times 30 \text{ minutes}\)

\(\text{Distance} = 3000 \text{ m}\)

5. Convert the Distance from Meters to Kilometers

The question asks for the distance in kilometers. There are 1000 meters in 1 kilometer. To convert meters to kilometers, we divide the distance in meters by 1000.

\(\text{Distance in km} = \frac{\text{Distance in meters}}{1000}\)

\(\text{Distance in km} = \frac{3000 \text{ m}}{1000 \text{ m/km}}\)

\(\text{Distance in km} = 3 \text{ km}\)

Therefore, the cyclist would cover 3 kilometers in half an hour at the same speed.

Summary of Calculations

The calculated distance of 3 km matches one of the provided options.

Revision Table: Speed, Distance, Time Concepts

Additional Information: Unit Conversions for Distance and Time

It is crucial to use consistent units when solving problems involving speed, distance, and time. If units are mixed (e.g., distance in meters, time in hours), one must be converted. Common conversions include:

• Distance:
  • 1 kilometer (km) = 1000 meters (m)
  • 1 meter (m) = 100 centimeters (cm)
• Time:
  • 1 hour = 60 minutes
  • 1 minute = 60 seconds
  • 1 hour = 3600 seconds

In this problem, we converted minutes to minutes (30 minutes from half an hour) and then meters to kilometers at the end to meet the required unit for the final answer.