Calculating Average Speed for Journey Planning

This problem involves calculating distances covered at different speeds and then determining the required speed for the remaining part of a journey based on a total planned distance.

Step-by-Step Calculation of Distances

First, let's calculate the distance covered in each part of Kapil's journey.

Part 1: Distance Calculation

• Time taken: 4.5 hours
• Speed: 50 km/h
• Distance covered (Distance 1): Speed $\times$ Time

$\text{Distance } 1 = 50 \text{ km/h} \times 4.5 \text{ hours}$
$\text{Distance } 1 = 225 \text{ km}$

Part 2: Distance Calculation

• Time taken: 7.5 hours
• Speed: 70 km/h
• Distance covered (Distance 2): Speed $\times$ Time

$\text{Distance } 2 = 70 \text{ km/h} \times 7.5 \text{ hours}$
$\text{Distance } 2 = 525 \text{ km}$

Total Distance Covered So Far

The total distance covered in these two parts is the sum of Distance 1 and Distance 2.

$\text{Total Covered Distance} = \text{Distance } 1 + \text{Distance } 2$
$\text{Total Covered Distance} = 225 \text{ km} + 525 \text{ km}$
$\text{Total Covered Distance} = 750 \text{ km}$

Determining the Total Planned Distance

The problem states that the 750 km covered is only $\frac{6}{7}$ of the total planned distance.

Let the total planned distance be $D$ km.

According to the problem:

$\frac{6}{7} \times D = 750 \text{ km}$

To find the total planned distance $D$, we can rearrange the equation:

$D = 750 \times \frac{7}{6}$
$D = (125 \times 6) \times \frac{7}{6}$
$D = 125 \times 7$
$D = 875 \text{ km}$

The total planned distance was 875 km.

Calculating the Remaining Distance

The remaining distance is the difference between the total planned distance and the total distance covered so far.

$\text{Remaining Distance} = \text{Total Planned Distance} - \text{Total Covered Distance}$
$\text{Remaining Distance} = 875 \text{ km} - 750 \text{ km}$
$\text{Remaining Distance} = 125 \text{ km}$

Calculating the Required Average Speed

Kapil needs to travel the remaining 125 km in 5 hours. To find the required average speed, we use the formula: Speed = Distance / Time.

• Remaining Distance: 125 km
• Time available: 5 hours

$\text{Required Average Speed} = \frac{\text{Remaining Distance}}{\text{Time Available}}$
$\text{Required Average Speed} = \frac{125 \text{ km}}{5 \text{ hours}}$
$\text{Required Average Speed} = 25 \text{ km/h}$

So, Kapil should travel at an average speed of 25 km/h to cover the remaining distance in 5 hours.

Revision Table: Speed, Distance, Time

Understanding the relationship between speed, distance, and time is crucial for solving such problems. Here's a quick review:

• Speed: How fast an object is moving. Measured in units like km/h or m/s. Formula: $\text{Speed} = \frac{\text{Distance}}{\text{Time}}$.
• Distance: The total length covered during motion. Measured in units like km or meters. Formula: $\text{Distance} = \text{Speed} \times \text{Time}$.
• Time: The duration of the motion. Measured in units like hours or seconds. Formula: $\text{Time} = \frac{\text{Distance}}{\text{Speed}}$.

Remember these basic formulas to tackle any problem involving these three quantities.

Additional Information: Average Speed Concepts

Average speed is not always simply the average of different speeds. It is defined as the total distance traveled divided by the total time taken for the journey.

$\text{Average Speed} = \frac{\text{Total Distance Traveled}}{\text{Total Time Taken}}$

In this problem, when calculating the speed for the remaining distance, we used the definition of average speed for that specific segment: remaining distance divided by the time allotted for that segment.

Understanding the total distance and total time is key to calculating the overall average speed of a journey, which would be different from the average speed of a specific segment.