A car covers a distace of 480 km at a uniform speed. If the speed of the car is 20 km/hour more, it takes 2 hours less to cover the same distance. What was the original speed of the car?

Options

A. 45km/hr
B. 50km/hr
C. 60km/hr
D. 70km/hr

Answer

To solve the problem step-by-step, we will denote the original speed of the car as \( V \) km/h.

### Step 1: Write the equation for time taken at original speed
The time taken to cover 480 km at the original speed \( V \) is given by:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{480}{V} \]

### Step 2: Write the equation for time taken at increased speed
If the speed of the car is increased by 20 km/h, the new speed becomes \( V + 20 \) km/h. The time taken to cover the same distance at this new speed is:
\[ \text{Time} = \frac{480}{V + 20} \]

### Step 3: Set up the equation based on the time difference
According to the problem, when the speed is increased by 20 km/h, it takes 2 hours less. Therefore, we can set up the following equation:
\[ \frac{480}{V} - \frac{480}{V + 20} = 2 \]

### Step 4: Clear the fractions by multiplying through by \( V(V + 20) \)
To eliminate the fractions, multiply both sides of the equation by \( V(V + 20) \):
\[ 480(V + 20) - 480V = 2V(V + 20) \]

### Step 5: Simplify the equation
Expanding both sides gives:
\[ 480V + 9600 - 480V = 2V^2 + 40V \]
This simplifies to:
\[ 9600 = 2V^2 + 40V \]

### Step 6: Rearrange the equation into standard quadratic form
Rearranging gives:
\[ 2V^2 + 40V - 9600 = 0 \]
Dividing the entire equation by 2 simplifies it to:
\[ V^2 + 20V - 4800 = 0 \]

### Step 7: Factor the quadratic equation
To factor the quadratic equation \( V^2 + 20V - 4800 = 0 \), we look for two numbers that multiply to \(-4800\) and add to \(20\). The factors are \(80\) and \(-60\):
\[ (V + 80)(V - 60) = 0 \]

### Step 8: Solve for V
Setting each factor equal to zero gives:
\[ V + 80 = 0 \quad \text{or} \quad V - 60 = 0 \]
Thus, we find:
\[ V = -80 \quad \text{or} \quad V = 60 \]
Since speed cannot be negative, we take \( V = 60 \) km/h.

### Final Answer
The original speed of the car is \( \boxed{60} \) km/h.

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