The difference between the time taken by two cars to travel a distance of 280 km is 1 hr 36 minutes. If the difference between their speed is 20 kmph, Find the speed of slower car.(in kmph)

Options

A. A)40
B. B)60
C. C)80
D. D)50

Answer

To solve the problem step by step, we will use the information given about the distance, the time difference, and the speed difference between the two cars.

### Step 1: Understand the given information
- Distance (D) = 280 km
- Time difference (T) = 1 hour 36 minutes = 96 minutes
- Speed difference (ΔS) = 20 km/h

### Step 2: Convert the time difference into hours
Since speed is in km/h, we need to convert the time difference from minutes to hours:
- 96 minutes = \( \frac{96}{60} \) hours = \( \frac{16}{10} \) hours = \( \frac{8}{5} \) hours.

### Step 3: Set up the equations
Let the speed of the slower car be \( V \) km/h. Then the speed of the faster car will be \( V + 20 \) km/h.

### Step 4: Write the time taken by each car
- Time taken by the slower car = \( \frac{280}{V} \)
- Time taken by the faster car = \( \frac{280}{V + 20} \)

### Step 5: Set up the equation based on the time difference
The difference in time taken by the two cars is given as 1 hour 36 minutes (or \( \frac{8}{5} \) hours):
\[ \frac{280}{V} - \frac{280}{V + 20} = \frac{8}{5} \]

### Step 6: Solve the equation
To solve the equation, we can find a common denominator and simplify:
\[ \frac{280(V + 20) - 280V}{V(V + 20)} = \frac{8}{5} \]
This simplifies to:
\[ \frac{5600}{V(V + 20)} = \frac{8}{5} \]

### Step 7: Cross-multiply to eliminate the fraction
Cross-multiplying gives:
\[ 5600 \cdot 5 = 8 \cdot V(V + 20) \]
\[ 28000 = 8V^2 + 160V \]

### Step 8: Rearrange the equation
Rearranging gives us a standard quadratic equation:
\[ 8V^2 + 160V - 28000 = 0 \]
Dividing the entire equation by 8 simplifies it:
\[ V^2 + 20V - 3500 = 0 \]

### Step 9: Factor the quadratic equation
We need to factor the quadratic equation:
\[ (V + 70)(V - 50) = 0 \]
This gives us two possible solutions for \( V \):
1. \( V = -70 \) (not valid since speed cannot be negative)
2. \( V = 50 \) (valid solution)

### Step 10: Conclusion
The speed of the slower car is \( 50 \) km/h.