A car travels a certain distance at a speed of 120km/hr in 4 hours. What should be the speed of the car if the car covers the same distance in 3 hours 20 minutes.

Options

A. 142 km/hr
B. 140 km/hr
C. 124 km/hr
D. 144 km/hr

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Calculate the distance traveled by the car.
The formula for distance is:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]

Given:
- Speed = 120 km/hr
- Time = 4 hours

So, the distance \( d \) is:
\[ d = 120 \, \text{km/hr} \times 4 \, \text{hr} = 480 \, \text{km} \]

### Step 2: Convert the time of 3 hours 20 minutes into hours.
To convert minutes into hours:
- 20 minutes = \( \frac{20}{60} \) hours = \( \frac{1}{3} \) hours.

Thus,
\[ 3 \, \text{hours} + \frac{1}{3} \, \text{hours} = 3 + \frac{1}{3} = \frac{9}{3} + \frac{1}{3} = \frac{10}{3} \, \text{hours} \]

### Step 3: Calculate the speed required to cover the same distance in 3 hours 20 minutes.
Using the formula for speed:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]

We already calculated the distance as 480 km and the time as \( \frac{10}{3} \) hours.

So, the speed \( v \) is:
\[ v = \frac{480 \, \text{km}}{\frac{10}{3} \, \text{hours}} \]

To simplify this, we multiply by the reciprocal of \( \frac{10}{3} \):
\[ v = 480 \, \text{km} \times \frac{3}{10} = \frac{1440}{10} = 144 \, \text{km/hr} \]

### Final Answer:
The speed of the car should be **144 km/hr**.

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