Solving Distance, Speed, and Time Problems

This problem involves calculating the required speed to cover a remaining distance within a remaining time, given the total distance, total time, and the speed and time spent on the initial part of the journey.

We are given the following information:

• Total distance to cover: 150 km
• Total time available: 15 hours
• Speed for the first part: 11.8 km/hr
• Time spent on the first part: 10 hours

We need to find the speed required to cover the remaining distance in the remaining time.

Step-by-Step Calculation

1. Calculate the distance covered in the first part of the journey.

The distance covered in the first part can be calculated using the formula: Distance = Speed × Time.

Distance covered in the first part = \(11.8 \text{ km/hr} \times 10 \text{ hours}\)

Distance covered = \(118 \text{ km}\)

2. Calculate the remaining distance to be covered.

The remaining distance is the total distance minus the distance already covered.

Remaining distance = Total distance - Distance covered in the first part

Remaining distance = \(150 \text{ km} - 118 \text{ km}\)

Remaining distance = \(32 \text{ km}\)

3. Calculate the remaining time available.

The remaining time is the total time available minus the time already spent.

Remaining time = Total time - Time spent on the first part

Remaining time = \(15 \text{ hours} - 10 \text{ hours}\)

Remaining time = \(5 \text{ hours}\)

4. Calculate the required speed for the remaining distance.

The required speed is the remaining distance divided by the remaining time.

Required speed = Remaining distance / Remaining time

Required speed = \(32 \text{ km} / 5 \text{ hours}\)

Required speed = \(6.4 \text{ km/hr}\)

So, the person has to travel at a speed of 6.4 km/hr to cover the remaining distance in the remaining time.

Summary of Calculations

Understanding Distance, Speed, and Time Relationship

The fundamental relationship between distance, speed, and time is given by the formula:

\[ \text{Distance} = \text{Speed} \times \text{Time} \]

This formula can be rearranged to find speed or time:

• \[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]

• \[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

In problems like this, where the journey is divided into parts, we analyze each part separately and then use the remaining quantities to calculate the required value for the subsequent part.

Revision Table: Key Concepts

Additional Information: Problem Solving Tips

• Always read the question carefully to identify the given values and what needs to be found.
• Break down complex problems into smaller, manageable steps.
• Keep track of units (km, km/hr, hours) to ensure consistency in calculations.
• Use the appropriate formula for distance, speed, or time based on what you need to calculate.