\( 50 \quad \) A man drove for 4hours at a certain speed, he then doubled his speed and drove for another 3 hours. Altogether he covered 600 km . At what speed did he drive for the last 3 hours? \( \begin{array}{lll}\text { A. } 120 \mathrm{~km} / \mathrm{hr} & \text { B. } 60 \mathrm{~km} / \mathrm{hr} & \text { C. } 600 / 7 \mathrm{~km} / \mathrm{hr} \\ \text { D. } 50 \mathrm{~km} / \mathrm{hr} & \text { E. } 100 \mathrm{~km} / \mathrm{hr}\end{array} \)

Let's break it down! The man drives for 4 hours at a speed of \( x \) km/h. So the distance covered in the first part is \( 4x \) km. Next, he doubles his speed to \( 2x \) km/h and drives for 3 hours, covering \( 6x \) km. The total distance is the sum of both parts, which equals 600 km. Setting up the equation: \[ 4x + 6x = 600 \] This simplifies to: \[ 10x = 600 \] So, \( x = 60 \) km/h. Therefore, in the last 3 hours, he drove at \( 2x = 120 \) km/h. So the speed he drove for the last 3 hours is \( 120 \) km/h! The correct answer is: A. 120 km/hr. Following this logic, it's crucial to remember that when working with distances and speeds, it's all about the relationship between time, speed, and distance. If you set up your equations correctly, the rest will follow smoothly!