(b) A man drives from Ibadan to Oyo, a distance of 48 km in 45 minutês. If he drives at \( 72 \mathrm{~km} / \mathrm{h} \) where the surface is good and \( 48 \mathrm{~km} / / \mathrm{wh} \) where it is bad, find the number of kilometres of good surface.

To solve this problem, we need to set up equations based on the distances traveled on good and bad surfaces. Let \( x \) be the distance (in km) on good surface, and \( 48 - x \) be the distance on bad surface. Using the speed formula \( \text{Distance} = \text{Speed} \times \text{Time} \): 1. The time for the distance on good surface is \( \frac{x}{72} \) hours. 2. The time for the distance on bad surface is \( \frac{48 - x}{48} \) hours. Since the total driving time is 45 minutes (which is \( \frac{3}{4} \) hours), we can write the equation: \[ \frac{x}{72} + \frac{48 - x}{48} = \frac{3}{4} \] Next, we find a common denominator, which is \( 144 \): \[ \frac{2x}{144} + \frac{3(48 - x)}{144} = \frac{3}{4} \] Multiplying through by 144 gives: \[ 2x + 144 - 3x = 108 \] Rearranging gives: \[ -x + 144 = 108 \\ -x = -36 \\ x = 36 \] Thus, the distance of good surface is \( \boxed{36} \) km. The distance of bad surface would be \( 48 - 36 = 12 \) km. So, our final answer: 36 km of good surface! Now, let's add some context and tips. The role of infrastructure improvement can't be overlooked; it significantly influences driving conditions and times. In many parts of Nigeria, both new and old roads continuously evolve. The better surfaces reduce travel time and are essential for connecting cities and boosting commerce. Remember, when approaching similar problems, always double-check the units you are working with! Converting time from minutes to hours can make or break your calculations. Also, mixing speeds and distances without clarifying your variables can lead to confusion. Stay organized, and you’ll be cruising smoothly!