The distance between two places is 200 km. The time taken to travel from one place to the other by a motor car is 2 hours more than the time taken by a jeep. The speed of the jeep is 5 km/h more than that of the motor car. Find the speed of the motor car.

Q.The distance between two places is 200 km. The time taken to travel from one place to the other by a motor car is 2 hours more than the time taken by a jeep. The speed of the jeep is 5 km/h more than that of the motor car. Find the speed of the motor car.

Let the speed of the motor car be \(x\) km/h. \[ \therefore \text{Speed of the jeep} = (x + 5) \text{ km/h} \] Time taken by the motor car to cover 200 km = \(\frac{200}{x}\) hours Time taken by the jeep to cover 200 km = \(\frac{200}{x + 5}\) hours According to the condition: \[ \frac{200}{x + 5} = \frac{200}{x} - 2 \] \[ \Rightarrow \frac{200}{x + 5} = \frac{200 - 2x}{x} \] \[ \Rightarrow 200x = (200 - 2x)(x + 5) \] \[ \Rightarrow 200x = 200x + 1000 - 2x^2 - 10x \] \[ \Rightarrow 200x - 200x - 1000 + 2x^2 + 10x = 0 \] \[ \Rightarrow 2x^2 + 10x - 1000 = 0 \] \[ \Rightarrow x^2 + 5x - 500 = 0 \] \[ \Rightarrow x^2 + 25x - 20x - 500 = 0 \] \[ \Rightarrow x(x + 25) - 20(x + 25) = 0 \] \[ \Rightarrow (x + 25)(x - 20) = 0 \] So, either \(x + 25 = 0 \Rightarrow x = -25\) or \(x - 20 = 0 \Rightarrow x = 20\) Since speed cannot be negative, \[ \therefore x = 20 \] Hence, the speed of the motor car is 20 km/h.