Let's solve this problem step-by-step using the relationship between distance, speed, and time.

Understanding the Problem: Car Speed, Distance, and Time

We are given the initial distance covered by a car and the time taken. We need to find the time taken to cover double that distance when the car's speed is increased by 20%.

Initial Scenario: Calculating the Car's Original Speed

The formula connecting distance, speed, and time is:

Speed = Distance / Time

In the initial scenario:

• Initial Distance = 144 km
• Initial Time = 1.8 hours

Let's calculate the initial speed of the car.

Initial Speed $= \frac{144 \text{ km}}{1.8 \text{ hours}}$

To make the division easier, we can remove the decimal from the denominator by multiplying both numerator and denominator by 10:

Initial Speed $= \frac{144 \times 10}{1.8 \times 10} = \frac{1440}{18}$

Dividing 1440 by 18:

Initial Speed $= 80 \text{ km/hour}$

Calculating the New Speed after Increase

The problem states that the car's speed is increased by 20%.

Increase in Speed = 20% of Initial Speed

Increase in Speed $= \frac{20}{100} \times 80 \text{ km/hour}$

Increase in Speed $= 0.20 \times 80 \text{ km/hour}$

Increase in Speed $= 16 \text{ km/hour}$

The New Speed will be the Initial Speed plus the Increase in Speed.

New Speed = Initial Speed + Increase in Speed

New Speed $= 80 \text{ km/hour} + 16 \text{ km/hour}$

New Speed $= 96 \text{ km/hour}$

Calculating the New Distance to be Covered

The question asks for the time taken to cover double the initial distance.

Initial Distance = 144 km

New Distance = $2 \times$ Initial Distance

New Distance $= 2 \times 144 \text{ km}$

New Distance $= 288 \text{ km}$

Finding the Time to Cover the New Distance with the New Speed

Now we have the New Distance and the New Speed, and we need to find the time taken. We use the same formula, rearranged to find time:

Time = Distance / Speed

Using the new values:

• New Distance = 288 km
• New Speed = 96 km/hour

Time $= \frac{288 \text{ km}}{96 \text{ km/hour}}$

Time $= 3 \text{ hours}$

So, the car will cover double the distance (288 km) in 3 hours when its speed is increased by 20% (to 96 km/hour).

Here is a summary of the values:

The calculated time is 3 hours.

Revision Table: Car Speed and Time Calculation

Additional Information: Speed, Distance, Time Concepts

• The relationship Distance = Speed $\times$ Time is fundamental in physics and mathematics for problems involving motion.
• If speed is constant, distance is directly proportional to time. Doubling the distance would double the time.
• If time is constant, distance is directly proportional to speed. Doubling the speed would double the distance covered in the same time.
• If distance is constant, speed is inversely proportional to time. Doubling the speed would halve the time taken to cover the same distance.
• Percentage increase means adding a fraction of the original value to the original value. A 20% increase means the new value is 120% of the original value ($1 + 0.20 = 1.20$). So, New Speed = $1.20 \times$ Initial Speed. $1.20 \times 80 = 96$ km/h, which matches our calculation.