Question

A car travels 240 km in 4 hours. If it continues at the same speed, how much distance will it cover in 7 hours?

• A. 360 km
• B. 380 km
• C. 420 km
• D. 450 km

Hint:

Under constant speed, the ratio of time is \(4 : 7\), so the ratio of distance must also be \(4 : 7\).
Since 4 units of distance = 240 km, then 1 unit = 60 km.
Therefore, 7 units of distance = \(7 \times 60\) = 420 km. This ratio technique avoids complex calculations.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
This is a motion problem involving Speed, Distance, and Time. We are given the distance traveled by a car in 4 hours and need to determine the total distance it will cover in 7 hours, assuming it travels at the same uniform speed.

Step 2: Key Formula or Approach:
• We can solve this either by calculating the Speed first or by using the Direct Proportionality of distance and time when speed is constant.
- Formula 1: \[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \] - Formula 2: \[ \text{Distance} = \text{Speed} \times \text{Time} \] - Formula 3 (Direct Proportion): Since speed is constant, the ratio of distance to time remains constant:
\[ \frac{D_1}{T_1} = \frac{D_2}{T_2} \]

Step 3: Detailed Explanation:

• Method 1: Two-step Speed Calculation Method
1. Identify the initial values: - Initial Distance (\(D_1\)) = 240 km - Initial Time (\(T_1\)) = 4 hours 2. Compute the constant speed of the car: \[ \text{Speed} = \frac{D_1}{T_1} = \frac{240 \text{ km}}{4 \text{ hours}} = 60 \text{ km/h} \] 3. Calculate the distance covered in the new time frame (\(T_2 = 7\) hours) using the calculated speed: \[ D_2 = \text{Speed} \times T_2 \] \[ D_2 = 60 \text{ km/h} \times 7 \text{ hours} = 420 \text{ km} \]
• Method 2: Direct Proportion Method (Unitary Method)
1. Since the speed remains unchanged, distance covered is directly proportional to time: \[ \frac{240}{4} = \frac{D_2}{7} \] 2. Simplify the left side of the equation: \[ 60 = \frac{D_2}{7} \] 3. Solve for \(D_2\): \[ D_2 = 60 \times 7 = 420 \text{ km} \] - Both methods yield the identical answer of 420 km.

Step 4: Final Answer:
The car will cover a distance of 420 km in 7 hours. Hence, the correct option is (C).